R.<x,v,b,r,j> = PowerSeriesRing(QQ, default_prec=30)
simplify(expand(exp(x*v*(1+Sr)*(1+Sb)*(1+Sj)))-1-Sv)
======================================================================
n=1
(1,0,0) -> 1
n=2
(2, 2, 0, 0): 1,
(2, 1, 1, 0): 2,
(2, 1, 0, 1): 2,
n=3
(3, 3, 0, 0) -> 1 = 1 ,
(3, 2, 1, 0) -> 12 = 2^2 * 3 ,
(3, 2, 0, 1) -> 12 = 2^2 * 3 ,
(3, 1, 2, 0) -> 3 = 3 ,
(3, 1, 1, 1) -> 18 = 2 * 3^2 ,
(3, 1, 0, 2) -> 3 = 3 ,
n=4
(4, 4, 0, 0) -> 1 = 1 ,
(4, 3, 1, 0) -> 48 = 2^4 * 3 ,
(4, 3, 0, 1) -> 48 = 2^4 * 3 ,
(4, 2, 2, 0) -> 72 = 2^3 * 3^2 ,
(4, 2, 1, 1) -> 288 = 2^5 * 3^2 ,
(4, 2, 0, 2) -> 72 = 2^3 * 3^2 ,
(4, 1, 3, 0) -> 4 = 2^2 ,
(4, 1, 2, 1) -> 96 = 2^5 * 3 ,
(4, 1, 1, 2) -> 96 = 2^5 * 3 ,
(4, 1, 0, 3) -> 4 = 2^2 ,
n=5
(5, 5, 0, 0) -> 1 = 1 ,
(5, 4, 1, 0) -> 160 = 2^5 * 5 ,
(5, 4, 0, 1) -> 160 = 2^5 * 5 ,
(5, 3, 2, 0) -> 810 = 2 * 3^4 * 5 ,
(5, 3, 1, 1) -> 2700 = 2^2 * 3^3 * 5^2 ,
(5, 3, 0, 2) -> 810 = 2 * 3^4 * 5 ,
(5, 2, 3, 0) -> 320 = 2^6 * 5 ,
(5, 2, 2, 1) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 1, 2) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 0, 3) -> 320 = 2^6 * 5 ,
(5, 1, 4, 0) -> 5 = 5 ,
(5, 1, 3, 1) -> 400 = 2^4 * 5^2 ,
(5, 1, 2, 2) -> 1350 = 2 * 3^3 * 5^2 ,
(5, 1, 1, 3) -> 400 = 2^4 * 5^2 ,
(5, 1, 0, 4) -> 5 = 5 ,
n=6
(6, 6, 0, 0) -> 1 = 1 ,
(6, 5, 1, 0) -> 480 = 2^5 * 3 * 5 ,
(6, 5, 0, 1) -> 480 = 2^5 * 3 * 5 ,
(6, 4, 2, 0) -> 6480 = 2^4 * 3^4 * 5 ,
(6, 4, 1, 1) -> 19440 = 2^4 * 3^5 * 5 ,
(6, 4, 0, 2) -> 6480 = 2^4 * 3^4 * 5 ,
(6, 3, 3, 0) -> 8640 = 2^6 * 3^3 * 5 ,
(6, 3, 2, 1) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 1, 2) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 0, 3) -> 8640 = 2^6 * 3^3 * 5 ,
(6, 2, 4, 0) -> 1200 = 2^4 * 3 * 5^2 ,
(6, 2, 3, 1) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 2, 2) -> 86400 = 2^7 * 3^3 * 5^2 ,
(6, 2, 1, 3) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 0, 4) -> 1200 = 2^4 * 3 * 5^2 ,
(6, 1, 5, 0) -> 6 = 2 * 3 ,
(6, 1, 4, 1) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 3, 2) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 2, 3) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 1, 4) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 0, 5) -> 6 = 2 * 3 ,
n=7
(7, 7, 0, 0) -> 1 = 1 ,
(7, 6, 1, 0) -> 1344 = 2^6 * 3 * 7 ,
(7, 6, 0, 1) -> 1344 = 2^6 * 3 * 7 ,
(7, 5, 2, 0) -> 42525 = 3^5 * 5^2 * 7 ,
(7, 5, 1, 1) -> 119070 = 2 * 3^5 * 5 * 7^2 ,
(7, 5, 0, 2) -> 42525 = 3^5 * 5^2 * 7 ,
(7, 4, 3, 0) -> 143360 = 2^12 * 5 * 7 ,
(7, 4, 2, 1) -> 940800 = 2^8 * 3 * 5^2 * 7^2 ,
(7, 4, 1, 2) -> 940800 = 2^8 * 3 * 5^2 * 7^2 ,
(7, 4, 0, 3) -> 143360 = 2^12 * 5 * 7 ,
(7, 3, 4, 0) -> 70875 = 3^4 * 5^3 * 7 ,
(7, 3, 3, 1) -> 1176000 = 2^6 * 3 * 5^3 * 7^2 ,
(7, 3, 2, 2) -> 2756250 = 2 * 3^2 * 5^5 * 7^2 ,
(7, 3, 1, 3) -> 1176000 = 2^6 * 3 * 5^3 * 7^2 ,
(7, 3, 0, 4) -> 70875 = 3^4 * 5^3 * 7 ,
(7, 2, 5, 0) -> 4032 = 2^6 * 3^2 * 7 ,
(7, 2, 4, 1) -> 238140 = 2^2 * 3^5 * 5 * 7^2 ,
(7, 2, 3, 2) -> 1411200 = 2^7 * 3^2 * 5^2 * 7^2 ,
(7, 2, 2, 3) -> 1411200 = 2^7 * 3^2 * 5^2 * 7^2 ,
(7, 2, 1, 4) -> 238140 = 2^2 * 3^5 * 5 * 7^2 ,
(7, 2, 0, 5) -> 4032 = 2^6 * 3^2 * 7 ,
(7, 1, 6, 0) -> 7 = 7 ,
(7, 1, 5, 1) -> 4704 = 2^5 * 3 * 7^2 ,
(7, 1, 4, 2) -> 99225 = 3^4 * 5^2 * 7^2 ,
(7, 1, 3, 3) -> 250880 = 2^10 * 5 * 7^2 ,
(7, 1, 2, 4) -> 99225 = 3^4 * 5^2 * 7^2 ,
(7, 1, 1, 5) -> 4704 = 2^5 * 3 * 7^2 ,
(7, 1, 0, 6) -> 7 = 7 ,
n=8
(8, 8, 0, 0) -> 1 = 1 ,
(8, 7, 1, 0) -> 3584 = 2^9 * 7 ,
(8, 7, 0, 1) -> 3584 = 2^9 * 7 ,
(8, 6, 2, 0) -> 244944 = 2^4 * 3^7 * 7 ,
(8, 6, 1, 1) -> 653184 = 2^7 * 3^6 * 7 ,
(8, 6, 0, 2) -> 244944 = 2^4 * 3^7 * 7 ,
(8, 5, 3, 0) -> 1792000 = 2^11 * 5^3 * 7 ,
(8, 5, 2, 1) -> 10321920 = 2^15 * 3^2 * 5 * 7 ,
(8, 5, 1, 2) -> 10321920 = 2^15 * 3^2 * 5 * 7 ,
(8, 5, 0, 3) -> 1792000 = 2^11 * 5^3 * 7 ,
(8, 4, 4, 0) -> 2240000 = 2^9 * 5^4 * 7 ,
(8, 4, 3, 1) -> 28000000 = 2^8 * 5^6 * 7 ,
(8, 4, 2, 2) -> 60480000 = 2^9 * 3^3 * 5^4 * 7 ,
(8, 4, 1, 3) -> 28000000 = 2^8 * 5^6 * 7 ,
(8, 4, 0, 4) -> 2240000 = 2^9 * 5^4 * 7 ,
(8, 3, 5, 0) -> 489888 = 2^5 * 3^7 * 7 ,
(8, 3, 4, 1) -> 15482880 = 2^14 * 3^3 * 5 * 7 ,
(8, 3, 3, 2) -> 72576000 = 2^10 * 3^4 * 5^3 * 7 ,
(8, 3, 2, 3) -> 72576000 = 2^10 * 3^4 * 5^3 * 7 ,
(8, 3, 1, 4) -> 15482880 = 2^14 * 3^3 * 5 * 7 ,
(8, 3, 0, 5) -> 489888 = 2^5 * 3^7 * 7 ,
(8, 2, 6, 0) -> 12544 = 2^8 * 7^2 ,
(8, 2, 5, 1) -> 1524096 = 2^7 * 3^5 * 7^2 ,
(8, 2, 4, 2) -> 18063360 = 2^13 * 3^2 * 5 * 7^2 ,
(8, 2, 3, 3) -> 39200000 = 2^8 * 5^5 * 7^2 ,
(8, 2, 2, 4) -> 18063360 = 2^13 * 3^2 * 5 * 7^2 ,
(8, 2, 1, 5) -> 1524096 = 2^7 * 3^5 * 7^2 ,
(8, 2, 0, 6) -> 12544 = 2^8 * 7^2 ,
(8, 1, 7, 0) -> 8 = 2^3 ,
(8, 1, 6, 1) -> 14336 = 2^11 * 7 ,
(8, 1, 5, 2) -> 653184 = 2^7 * 3^6 * 7 ,
(8, 1, 4, 3) -> 3584000 = 2^12 * 5^3 * 7 ,
(8, 1, 3, 4) -> 3584000 = 2^12 * 5^3 * 7 ,
(8, 1, 2, 5) -> 653184 = 2^7 * 3^6 * 7 ,
(8, 1, 1, 6) -> 14336 = 2^11 * 7 ,
(8, 1, 0, 7) -> 8 = 2^3 ,
n=9
(9, 9, 0, 0) -> 1 = 1 ,
(9, 8, 1, 0) -> 9216 = 2^10 * 3^2 ,
(9, 8, 0, 1) -> 9216 = 2^10 * 3^2 ,
(9, 7, 2, 0) -> 1285956 = 2^2 * 3^8 * 7^2 ,
(9, 7, 1, 1) -> 3306744 = 2^3 * 3^10 * 7 ,
(9, 7, 0, 2) -> 1285956 = 2^2 * 3^8 * 7^2 ,
(9, 6, 3, 0) -> 18579456 = 2^15 * 3^4 * 7 ,
(9, 6, 2, 1) -> 97542144 = 2^13 * 3^5 * 7^2 ,
(9, 6, 1, 2) -> 97542144 = 2^13 * 3^5 * 7^2 ,
(9, 6, 0, 3) -> 18579456 = 2^15 * 3^4 * 7 ,
(9, 5, 4, 0) -> 49218750 = 2 * 3^2 * 5^8 * 7 ,
(9, 5, 3, 1) -> 510300000 = 2^5 * 3^6 * 5^5 * 7 ,
(9, 5, 2, 2) -> 1041862500 = 2^2 * 3^5 * 5^5 * 7^3 ,
(9, 5, 1, 3) -> 510300000 = 2^5 * 3^6 * 5^5 * 7 ,
(9, 5, 0, 4) -> 49218750 = 2 * 3^2 * 5^8 * 7 ,
(9, 4, 5, 0) -> 27869184 = 2^14 * 3^5 * 7 ,
(9, 4, 4, 1) -> 612360000 = 2^6 * 3^7 * 5^4 * 7 ,
(9, 4, 3, 2) -> 2469035520 = 2^9 * 3^9 * 5 * 7^2 ,
(9, 4, 2, 3) -> 2469035520 = 2^9 * 3^9 * 5 * 7^2 ,
(9, 4, 1, 4) -> 612360000 = 2^6 * 3^7 * 5^4 * 7 ,
(9, 4, 0, 5) -> 27869184 = 2^14 * 3^5 * 7 ,
(9, 3, 6, 0) -> 3000564 = 2^2 * 3^7 * 7^3 ,
(9, 3, 5, 1) -> 170698752 = 2^11 * 3^5 * 7^3 ,
(9, 3, 4, 2) -> 1458607500 = 2^2 * 3^5 * 5^4 * 7^4 ,
(9, 3, 3, 3) -> 2880541440 = 2^8 * 3^8 * 5 * 7^3 ,
(9, 3, 2, 4) -> 1458607500 = 2^2 * 3^5 * 5^4 * 7^4 ,
(9, 3, 1, 5) -> 170698752 = 2^11 * 3^5 * 7^3 ,
(9, 3, 0, 6) -> 3000564 = 2^2 * 3^7 * 7^3 ,
(9, 2, 7, 0) -> 36864 = 2^12 * 3^2 ,
(9, 2, 6, 1) -> 8817984 = 2^6 * 3^9 * 7 ,
(9, 2, 5, 2) -> 195084288 = 2^14 * 3^5 * 7^2 ,
(9, 2, 4, 3) -> 816480000 = 2^8 * 3^6 * 5^4 * 7 ,
(9, 2, 3, 4) -> 816480000 = 2^8 * 3^6 * 5^4 * 7 ,
(9, 2, 2, 5) -> 195084288 = 2^14 * 3^5 * 7^2 ,
(9, 2, 1, 6) -> 8817984 = 2^6 * 3^9 * 7 ,
(9, 2, 0, 7) -> 36864 = 2^12 * 3^2 ,
(9, 1, 8, 0) -> 9 = 3^2 ,
(9, 1, 7, 1) -> 41472 = 2^9 * 3^4 ,
(9, 1, 6, 2) -> 3857868 = 2^2 * 3^9 * 7^2 ,
(9, 1, 5, 3) -> 41803776 = 2^13 * 3^6 * 7 ,
(9, 1, 4, 4) -> 88593750 = 2 * 3^4 * 5^7 * 7 ,
(9, 1, 3, 5) -> 41803776 = 2^13 * 3^6 * 7 ,
(9, 1, 2, 6) -> 3857868 = 2^2 * 3^9 * 7^2 ,
(9, 1, 1, 7) -> 41472 = 2^9 * 3^4 ,
(9, 1, 0, 8) -> 9 = 3^2 ,
n=10
(10, 10, 0, 0) -> 1 = 1 ,
(10, 9, 1, 0) -> 23040 = 2^9 * 3^2 * 5 ,
(10, 9, 0, 1) -> 23040 = 2^9 * 3^2 * 5 ,
(10, 8, 2, 0) -> 6298560 = 2^6 * 3^9 * 5 ,
(10, 8, 1, 1) -> 15746400 = 2^5 * 3^9 * 5^2 ,
(10, 8, 0, 2) -> 6298560 = 2^6 * 3^9 * 5 ,
(10, 7, 3, 0) -> 168591360 = 2^15 * 3 * 5 * 7^3 ,
(10, 7, 2, 1) -> 825753600 = 2^19 * 3^2 * 5^2 * 7 ,
(10, 7, 1, 2) -> 825753600 = 2^19 * 3^2 * 5^2 * 7 ,
(10, 7, 0, 3) -> 168591360 = 2^15 * 3 * 5 * 7^3 ,
(10, 6, 4, 0) -> 850500000 = 2^5 * 3^5 * 5^6 * 7 ,
(10, 6, 3, 1) -> 7717500000 = 2^5 * 3^2 * 5^7 * 7^3 ,
(10, 6, 2, 2) -> 15120000000 = 2^10 * 3^3 * 5^7 * 7 ,
(10, 6, 1, 3) -> 7717500000 = 2^5 * 3^2 * 5^7 * 7^3 ,
(10, 6, 0, 4) -> 850500000 = 2^5 * 3^5 * 5^6 * 7 ,
(10, 5, 5, 0) -> 1020600000 = 2^6 * 3^6 * 5^5 * 7 ,
(10, 5, 4, 1) -> 17635968000 = 2^10 * 3^9 * 5^3 * 7 ,
(10, 5, 3, 2) -> 64012032000 = 2^11 * 3^6 * 5^3 * 7^3 ,
(10, 5, 2, 3) -> 64012032000 = 2^11 * 3^6 * 5^3 * 7^3 ,
(10, 5, 1, 4) -> 17635968000 = 2^10 * 3^9 * 5^3 * 7 ,
(10, 5, 0, 5) -> 1020600000 = 2^6 * 3^6 * 5^5 * 7 ,
(10, 4, 6, 0) -> 295034880 = 2^13 * 3 * 5 * 7^4 ,
(10, 4, 5, 1) -> 10804500000 = 2^5 * 3^2 * 5^6 * 7^4 ,
(10, 4, 4, 2) -> 74680704000 = 2^10 * 3^5 * 5^3 * 7^4 ,
(10, 4, 3, 3) -> 138355224000 = 2^6 * 3 * 5^3 * 7^8 ,
(10, 4, 2, 4) -> 74680704000 = 2^10 * 3^5 * 5^3 * 7^4 ,
(10, 4, 1, 5) -> 10804500000 = 2^5 * 3^2 * 5^6 * 7^4 ,
(10, 4, 0, 6) -> 295034880 = 2^13 * 3 * 5 * 7^4 ,
(10, 3, 7, 0) -> 16796160 = 2^9 * 3^8 * 5 ,
(10, 3, 6, 1) -> 1651507200 = 2^20 * 3^2 * 5^2 * 7 ,
(10, 3, 5, 2) -> 24192000000 = 2^13 * 3^3 * 5^6 * 7 ,
(10, 3, 4, 3) -> 85349376000 = 2^13 * 3^5 * 5^3 * 7^3 ,
(10, 3, 3, 4) -> 85349376000 = 2^13 * 3^5 * 5^3 * 7^3 ,
(10, 3, 2, 5) -> 24192000000 = 2^13 * 3^3 * 5^6 * 7 ,
(10, 3, 1, 6) -> 1651507200 = 2^20 * 3^2 * 5^2 * 7 ,
(10, 3, 0, 7) -> 16796160 = 2^9 * 3^8 * 5 ,
(10, 2, 8, 0) -> 103680 = 2^8 * 3^4 * 5 ,
(10, 2, 7, 1) -> 47239200 = 2^5 * 3^10 * 5^2 ,
(10, 2, 6, 2) -> 1857945600 = 2^17 * 3^4 * 5^2 * 7 ,
(10, 2, 5, 3) -> 13891500000 = 2^5 * 3^4 * 5^6 * 7^3 ,
(10, 2, 4, 4) -> 26453952000 = 2^9 * 3^10 * 5^3 * 7 ,
(10, 2, 3, 5) -> 13891500000 = 2^5 * 3^4 * 5^6 * 7^3 ,
(10, 2, 2, 6) -> 1857945600 = 2^17 * 3^4 * 5^2 * 7 ,
(10, 2, 1, 7) -> 47239200 = 2^5 * 3^10 * 5^2 ,
(10, 2, 0, 8) -> 103680 = 2^8 * 3^4 * 5 ,
(10, 1, 9, 0) -> 10 = 2 * 5 ,
(10, 1, 8, 1) -> 115200 = 2^9 * 3^2 * 5^2 ,
(10, 1, 7, 2) -> 20995200 = 2^7 * 3^8 * 5^2 ,
(10, 1, 6, 3) -> 421478400 = 2^14 * 3 * 5^2 * 7^3 ,
(10, 1, 5, 4) -> 1701000000 = 2^6 * 3^5 * 5^6 * 7 ,
(10, 1, 4, 5) -> 1701000000 = 2^6 * 3^5 * 5^6 * 7 ,
(10, 1, 3, 6) -> 421478400 = 2^14 * 3 * 5^2 * 7^3 ,
(10, 1, 2, 7) -> 20995200 = 2^7 * 3^8 * 5^2 ,
(10, 1, 1, 8) -> 115200 = 2^9 * 3^2 * 5^2 ,
(10, 1, 0, 9) -> 10 = 2 * 5 ,
n=11
(11, 11, 0, 0) -> 1 = 1 ,
(11, 10, 1, 0) -> 56320 = 2^10 * 5 * 11 ,
(11, 10, 0, 1) -> 56320 = 2^10 * 5 * 11 ,
(11, 9, 2, 0) -> 29229255 = 3^12 * 5 * 11 ,
(11, 9, 1, 1) -> 71449290 = 2 * 3^10 * 5 * 11^2 ,
(11, 9, 0, 2) -> 29229255 = 3^12 * 5 * 11 ,
(11, 8, 3, 0) -> 1384120320 = 2^23 * 3 * 5 * 11 ,
(11, 8, 2, 1) -> 6423183360 = 2^17 * 3^4 * 5 * 11^2 ,
(11, 8, 1, 2) -> 6423183360 = 2^17 * 3^4 * 5 * 11^2 ,
(11, 8, 0, 3) -> 1384120320 = 2^23 * 3 * 5 * 11 ,
(11, 7, 4, 0) -> 12380156250 = 2 * 3 * 5^7 * 7^4 * 11 ,
(11, 7, 3, 1) -> 101640000000 = 2^9 * 3 * 5^7 * 7 * 11^2 ,
(11, 7, 2, 2) -> 192957187500 = 2^2 * 3^6 * 5^7 * 7 * 11^2 ,
(11, 7, 1, 3) -> 101640000000 = 2^9 * 3 * 5^7 * 7 * 11^2 ,
(11, 7, 0, 4) -> 12380156250 = 2 * 3 * 5^7 * 7^4 * 11 ,
(11, 6, 5, 0) -> 27935373312 = 2^11 * 3^11 * 7 * 11 ,
(11, 6, 4, 1) -> 406636433280 = 2^7 * 3^7 * 5 * 7^4 * 11^2 ,
(11, 6, 3, 2) -> 1365729361920 = 2^14 * 3^9 * 5 * 7 * 11^2 ,
(11, 6, 2, 3) -> 1365729361920 = 2^14 * 3^9 * 5 * 7 * 11^2 ,
(11, 6, 1, 4) -> 406636433280 = 2^7 * 3^7 * 5 * 7^4 * 11^2 ,
(11, 6, 0, 5) -> 27935373312 = 2^11 * 3^11 * 7 * 11 ,
(11, 5, 6, 0) -> 17332218750 = 2 * 3 * 5^6 * 7^5 * 11 ,
(11, 5, 5, 1) -> 474409172160 = 2^6 * 3^6 * 5 * 7^5 * 11^2 ,
(11, 5, 4, 2) -> 2825040730050 = 2 * 3^4 * 5^2 * 7^8 * 11^2 ,
(11, 5, 3, 3) -> 4997890867200 = 2^15 * 3 * 5^2 * 7^5 * 11^2 ,
(11, 5, 2, 4) -> 2825040730050 = 2 * 3^4 * 5^2 * 7^8 * 11^2 ,
(11, 5, 1, 5) -> 474409172160 = 2^6 * 3^6 * 5 * 7^5 * 11^2 ,
(11, 5, 0, 6) -> 17332218750 = 2 * 3 * 5^6 * 7^5 * 11 ,
(11, 4, 7, 0) -> 2768240640 = 2^24 * 3 * 5 * 11 ,
(11, 4, 6, 1) -> 162624000000 = 2^12 * 3 * 5^6 * 7 * 11^2 ,
(11, 4, 5, 2) -> 1820972482560 = 2^16 * 3^8 * 5 * 7 * 11^2 ,
(11, 4, 4, 3) -> 5711875276800 = 2^18 * 3 * 5^2 * 7^4 * 11^2 ,
(11, 4, 3, 4) -> 5711875276800 = 2^18 * 3 * 5^2 * 7^4 * 11^2 ,
(11, 4, 2, 5) -> 1820972482560 = 2^16 * 3^8 * 5 * 7 * 11^2 ,
(11, 4, 1, 6) -> 162624000000 = 2^12 * 3 * 5^6 * 7 * 11^2 ,
(11, 4, 0, 7) -> 2768240640 = 2^24 * 3 * 5 * 11 ,
(11, 3, 8, 0) -> 87687765 = 3^13 * 5 * 11 ,
(11, 3, 7, 1) -> 14452162560 = 2^15 * 3^6 * 5 * 11^2 ,
(11, 3, 6, 2) -> 347322937500 = 2^2 * 3^8 * 5^6 * 7 * 11^2 ,
(11, 3, 5, 3) -> 2048594042880 = 2^13 * 3^10 * 5 * 7 * 11^2 ,
(11, 3, 4, 4) -> 3632195224350 = 2 * 3^6 * 5^2 * 7^7 * 11^2 ,
(11, 3, 3, 5) -> 2048594042880 = 2^13 * 3^10 * 5 * 7 * 11^2 ,
(11, 3, 2, 6) -> 347322937500 = 2^2 * 3^8 * 5^6 * 7 * 11^2 ,
(11, 3, 1, 7) -> 14452162560 = 2^15 * 3^6 * 5 * 11^2 ,
(11, 3, 0, 8) -> 87687765 = 3^13 * 5 * 11 ,
(11, 2, 9, 0) -> 281600 = 2^10 * 5^2 * 11 ,
(11, 2, 8, 1) -> 238164300 = 2^2 * 3^9 * 5^2 * 11^2 ,
(11, 2, 7, 2) -> 16057958400 = 2^16 * 3^4 * 5^2 * 11^2 ,
(11, 2, 6, 3) -> 203280000000 = 2^10 * 3 * 5^7 * 7 * 11^2 ,
(11, 2, 5, 4) -> 677727388800 = 2^7 * 3^6 * 5^2 * 7^4 * 11^2 ,
(11, 2, 4, 5) -> 677727388800 = 2^7 * 3^6 * 5^2 * 7^4 * 11^2 ,
(11, 2, 3, 6) -> 203280000000 = 2^10 * 3 * 5^7 * 7 * 11^2 ,
(11, 2, 2, 7) -> 16057958400 = 2^16 * 3^4 * 5^2 * 11^2 ,
(11, 2, 1, 8) -> 238164300 = 2^2 * 3^9 * 5^2 * 11^2 ,
(11, 2, 0, 9) -> 281600 = 2^10 * 5^2 * 11 ,
(11, 1, 10, 0) -> 11 = 11 ,
(11, 1, 9, 1) -> 309760 = 2^9 * 5 * 11^2 ,
(11, 1, 8, 2) -> 107173935 = 3^11 * 5 * 11^2 ,
(11, 1, 7, 3) -> 3806330880 = 2^21 * 3 * 5 * 11^2 ,
(11, 1, 6, 4) -> 27236343750 = 2 * 3 * 5^6 * 7^4 * 11^2 ,
(11, 1, 5, 5) -> 51214851072 = 2^10 * 3^10 * 7 * 11^2 ,
(11, 1, 4, 6) -> 27236343750 = 2 * 3 * 5^6 * 7^4 * 11^2 ,
(11, 1, 3, 7) -> 3806330880 = 2^21 * 3 * 5 * 11^2 ,
(11, 1, 2, 8) -> 107173935 = 3^11 * 5 * 11^2 ,
(11, 1, 1, 9) -> 309760 = 2^9 * 5 * 11^2 ,
(11, 1, 0, 10) -> 11 = 11 ,
n=12
(12, 12, 0, 0) -> 1 = 1 ,
(12, 11, 1, 0) -> 135168 = 2^12 * 3 * 11 ,
(12, 11, 0, 1) -> 135168 = 2^12 * 3 * 11 ,
(12, 10, 2, 0) -> 129907800 = 2^3 * 3^10 * 5^2 * 11 ,
(12, 10, 1, 1) -> 311778720 = 2^5 * 3^11 * 5 * 11 ,
(12, 10, 0, 2) -> 129907800 = 2^3 * 3^10 * 5^2 * 11 ,
(12, 9, 3, 0) -> 10510663680 = 2^18 * 3^6 * 5 * 11 ,
(12, 9, 2, 1) -> 46714060800 = 2^21 * 3^4 * 5^2 * 11 ,
(12, 9, 1, 2) -> 46714060800 = 2^21 * 3^4 * 5^2 * 11 ,
(12, 9, 0, 3) -> 10510663680 = 2^18 * 3^6 * 5 * 11 ,
(12, 8, 4, 0) -> 158400000000 = 2^12 * 3^2 * 5^8 * 11 ,
(12, 8, 3, 1) -> 1202850000000 = 2^7 * 3^7 * 5^8 * 11 ,
(12, 8, 2, 2) -> 2227500000000 = 2^8 * 3^4 * 5^10 * 11 ,
(12, 8, 1, 3) -> 1202850000000 = 2^7 * 3^7 * 5^8 * 11 ,
(12, 8, 0, 4) -> 158400000000 = 2^12 * 3^2 * 5^8 * 11 ,
(12, 7, 5, 0) -> 621044734464 = 2^9 * 3^8 * 7^5 * 11 ,
(12, 7, 4, 1) -> 7946061742080 = 2^20 * 3^9 * 5 * 7 * 11 ,
(12, 7, 3, 2) -> 25141835980800 = 2^13 * 3^13 * 5^2 * 7 * 11 ,
(12, 7, 2, 3) -> 25141835980800 = 2^13 * 3^13 * 5^2 * 7 * 11 ,
(12, 7, 1, 4) -> 7946061742080 = 2^20 * 3^9 * 5 * 7 * 11 ,
(12, 7, 0, 5) -> 621044734464 = 2^9 * 3^8 * 7^5 * 11 ,
(12, 6, 6, 0) -> 724552190208 = 2^8 * 3^7 * 7^6 * 11 ,
(12, 6, 5, 1) -> 16107868598976 = 2^6 * 3^4 * 7^10 * 11 ,
(12, 6, 4, 2) -> 85872852172800 = 2^15 * 3^4 * 5^2 * 7^6 * 11 ,
(12, 6, 3, 3) -> 146721818517120 = 2^7 * 3^11 * 5 * 7^6 * 11 ,
(12, 6, 2, 4) -> 85872852172800 = 2^15 * 3^4 * 5^2 * 7^6 * 11 ,
(12, 6, 1, 5) -> 16107868598976 = 2^6 * 3^4 * 7^10 * 11 ,
(12, 6, 0, 6) -> 724552190208 = 2^8 * 3^7 * 7^6 * 11 ,
(12, 5, 7, 0) -> 253440000000 = 2^15 * 3^2 * 5^7 * 11 ,
(12, 5, 6, 1) -> 10594748989440 = 2^22 * 3^8 * 5 * 7 * 11 ,
(12, 5, 5, 2) -> 98140402483200 = 2^18 * 3^4 * 5^2 * 7^5 * 11 ,
(12, 5, 4, 3) -> 282526639718400 = 2^26 * 3^7 * 5^2 * 7 * 11 ,
(12, 5, 3, 4) -> 282526639718400 = 2^26 * 3^7 * 5^2 * 7 * 11 ,
(12, 5, 2, 5) -> 98140402483200 = 2^18 * 3^4 * 5^2 * 7^5 * 11 ,
(12, 5, 1, 6) -> 10594748989440 = 2^22 * 3^8 * 5 * 7 * 11 ,
(12, 5, 0, 7) -> 253440000000 = 2^15 * 3^2 * 5^7 * 11 ,
(12, 4, 8, 0) -> 23648993280 = 2^16 * 3^8 * 5 * 11 ,
(12, 4, 7, 1) -> 2165130000000 = 2^7 * 3^9 * 5^7 * 11 ,
(12, 4, 6, 2) -> 37712753971200 = 2^12 * 3^14 * 5^2 * 7 * 11 ,
(12, 4, 5, 3) -> 188642338093440 = 2^7 * 3^13 * 5 * 7^5 * 11 ,
(12, 4, 4, 4) -> 317842469683200 = 2^23 * 3^9 * 5^2 * 7 * 11 ,
(12, 4, 3, 5) -> 188642338093440 = 2^7 * 3^13 * 5 * 7^5 * 11 ,
(12, 4, 2, 6) -> 37712753971200 = 2^12 * 3^14 * 5^2 * 7 * 11 ,
(12, 4, 1, 7) -> 2165130000000 = 2^7 * 3^9 * 5^7 * 11 ,
(12, 4, 0, 8) -> 23648993280 = 2^16 * 3^8 * 5 * 11 ,
(12, 3, 9, 0) -> 433026000 = 2^4 * 3^9 * 5^3 * 11 ,
(12, 3, 8, 1) -> 116785152000 = 2^20 * 3^4 * 5^3 * 11 ,
(12, 3, 7, 2) -> 4455000000000 = 2^9 * 3^4 * 5^10 * 11 ,
(12, 3, 6, 3) -> 41903059968000 = 2^13 * 3^12 * 5^3 * 7 * 11 ,
(12, 3, 5, 4) -> 122675503104000 = 2^16 * 3^4 * 5^3 * 7^5 * 11 ,
(12, 3, 4, 5) -> 122675503104000 = 2^16 * 3^4 * 5^3 * 7^5 * 11 ,
(12, 3, 3, 6) -> 41903059968000 = 2^13 * 3^12 * 5^3 * 7 * 11 ,
(12, 3, 2, 7) -> 4455000000000 = 2^9 * 3^4 * 5^10 * 11 ,
(12, 3, 1, 8) -> 116785152000 = 2^20 * 3^4 * 5^3 * 11 ,
(12, 3, 0, 9) -> 433026000 = 2^4 * 3^9 * 5^3 * 11 ,
(12, 2, 10, 0) -> 743424 = 2^11 * 3 * 11^2 ,
(12, 2, 9, 1) -> 1143188640 = 2^5 * 3^10 * 5 * 11^2 ,
(12, 2, 8, 2) -> 128463667200 = 2^19 * 3^4 * 5^2 * 11^2 ,
(12, 2, 7, 3) -> 2646270000000 = 2^7 * 3^7 * 5^7 * 11^2 ,
(12, 2, 6, 4) -> 14567779860480 = 2^19 * 3^8 * 5 * 7 * 11^2 ,
(12, 2, 5, 5) -> 25312364941248 = 2^6 * 3^4 * 7^9 * 11^2 ,
(12, 2, 4, 6) -> 14567779860480 = 2^19 * 3^8 * 5 * 7 * 11^2 ,
(12, 2, 3, 7) -> 2646270000000 = 2^7 * 3^7 * 5^7 * 11^2 ,
(12, 2, 2, 8) -> 128463667200 = 2^19 * 3^4 * 5^2 * 11^2 ,
(12, 2, 1, 9) -> 1143188640 = 2^5 * 3^10 * 5 * 11^2 ,
(12, 2, 0, 10) -> 743424 = 2^11 * 3 * 11^2 ,
(12, 1, 11, 0) -> 12 = 2^2 * 3 ,
(12, 1, 10, 1) -> 811008 = 2^13 * 3^2 * 11 ,
(12, 1, 9, 2) -> 519631200 = 2^5 * 3^10 * 5^2 * 11 ,
(12, 1, 8, 3) -> 31531991040 = 2^18 * 3^7 * 5 * 11 ,
(12, 1, 7, 4) -> 380160000000 = 2^14 * 3^3 * 5^7 * 11 ,
(12, 1, 6, 5) -> 1242089468928 = 2^10 * 3^8 * 7^5 * 11 ,
(12, 1, 5, 6) -> 1242089468928 = 2^10 * 3^8 * 7^5 * 11 ,
(12, 1, 4, 7) -> 380160000000 = 2^14 * 3^3 * 5^7 * 11 ,
(12, 1, 3, 8) -> 31531991040 = 2^18 * 3^7 * 5 * 11 ,
(12, 1, 2, 9) -> 519631200 = 2^5 * 3^10 * 5^2 * 11 ,
(12, 1, 1, 10) -> 811008 = 2^13 * 3^2 * 11 ,
(12, 1, 0, 11) -> 12 = 2^2 * 3 ,
n=13
(13, 13, 0, 0) -> 1 = 1 ,
(13, 12, 1, 0) -> 319488 = 2^13 * 3 * 13 ,
(13, 12, 0, 1) -> 319488 = 2^13 * 3 * 13 ,
(13, 11, 2, 0) -> 557304462 = 2 * 3^11 * 11^2 * 13 ,
(13, 11, 1, 1) -> 1317265092 = 2^2 * 3^11 * 11 * 13^2 ,
(13, 11, 0, 2) -> 557304462 = 2 * 3^11 * 11^2 * 13 ,
(13, 10, 3, 0) -> 74973184000 = 2^22 * 5^3 * 11 * 13 ,
(13, 10, 2, 1) -> 321634959360 = 2^20 * 3 * 5 * 11^2 * 13^2 ,
(13, 10, 1, 2) -> 321634959360 = 2^20 * 3 * 5 * 11^2 * 13^2 ,
(13, 10, 0, 3) -> 74973184000 = 2^22 * 5^3 * 11 * 13 ,
(13, 9, 4, 0) -> 1832466796875 = 3^8 * 5^9 * 11 * 13 ,
(13, 9, 3, 1) -> 13071093750000 = 2^4 * 3^2 * 5^11 * 11 * 13^2 ,
(13, 9, 2, 2) -> 23724035156250 = 2 * 3^3 * 5^9 * 11^3 * 13^2 ,
(13, 9, 1, 3) -> 13071093750000 = 2^4 * 3^2 * 5^11 * 11 * 13^2 ,
(13, 9, 0, 4) -> 1832466796875 = 3^8 * 5^9 * 11 * 13 ,
(13, 8, 5, 0) -> 11805577445376 = 2^22 * 3^9 * 11 * 13 ,
(13, 8, 4, 1) -> 136574044738560 = 2^10 * 3^15 * 5 * 11 * 13^2 ,
(13, 8, 3, 2) -> 412157611008000 = 2^13 * 3^9 * 5^3 * 11^2 * 13^2 ,
(13, 8, 2, 3) -> 412157611008000 = 2^13 * 3^9 * 5^3 * 11^2 * 13^2 ,
(13, 8, 1, 4) -> 136574044738560 = 2^10 * 3^15 * 5 * 11 * 13^2 ,
(13, 8, 0, 5) -> 11805577445376 = 2^22 * 3^9 * 11 * 13 ,
(13, 7, 6, 0) -> 23751648836916 = 2^2 * 3 * 7^12 * 11 * 13 ,
(13, 7, 5, 1) -> 451500373868544 = 2^15 * 3^2 * 7^7 * 11 * 13^2 ,
(13, 7, 4, 2) -> 2209827574494540 = 2^2 * 3^8 * 5 * 7^7 * 11^2 * 13^2 ,
(13, 7, 3, 3) -> 3674319448800000 = 2^8 * 3 * 5^5 * 7^7 * 11 * 13^2 ,
(13, 7, 2, 4) -> 2209827574494540 = 2^2 * 3^8 * 5 * 7^7 * 11^2 * 13^2 ,
(13, 7, 1, 5) -> 451500373868544 = 2^15 * 3^2 * 7^7 * 11 * 13^2 ,
(13, 7, 0, 6) -> 23751648836916 = 2^2 * 3 * 7^12 * 11 * 13 ,
(13, 6, 7, 0) -> 15740769927168 = 2^24 * 3^8 * 11 * 13 ,
(13, 6, 6, 1) -> 516000427278336 = 2^18 * 3^2 * 7^6 * 11 * 13^2 ,
(13, 6, 5, 2) -> 4149862899646464 = 2^30 * 3^3 * 7 * 11^2 * 13^2 ,
(13, 6, 4, 3) -> 11190703620096000 = 2^20 * 3^8 * 5^3 * 7 * 11 * 13^2 ,
(13, 6, 3, 4) -> 11190703620096000 = 2^20 * 3^8 * 5^3 * 7 * 11 * 13^2 ,
(13, 6, 2, 5) -> 4149862899646464 = 2^30 * 3^3 * 7 * 11^2 * 13^2 ,
(13, 6, 1, 6) -> 516000427278336 = 2^18 * 3^2 * 7^6 * 11 * 13^2 ,
(13, 6, 0, 7) -> 15740769927168 = 2^24 * 3^8 * 11 * 13 ,
(13, 5, 8, 0) -> 3298440234375 = 3^10 * 5^8 * 11 * 13 ,
(13, 5, 7, 1) -> 204861067107840 = 2^9 * 3^16 * 5 * 11 * 13^2 ,
(13, 5, 6, 2) -> 2841206881492980 = 2^2 * 3^10 * 5 * 7^6 * 11^2 * 13^2 ,
(13, 5, 5, 3) -> 12589541572608000 = 2^17 * 3^10 * 5^3 * 7 * 11 * 13^2 ,
(13, 5, 4, 4) -> 20418086434595850 = 2 * 3^22 * 5^2 * 7 * 11 * 13^2 ,
(13, 5, 3, 5) -> 12589541572608000 = 2^17 * 3^10 * 5^3 * 7 * 11 * 13^2 ,
(13, 5, 2, 6) -> 2841206881492980 = 2^2 * 3^10 * 5 * 7^6 * 11^2 * 13^2 ,
(13, 5, 1, 7) -> 204861067107840 = 2^9 * 3^16 * 5 * 11 * 13^2 ,
(13, 5, 0, 8) -> 3298440234375 = 3^10 * 5^8 * 11 * 13 ,
(13, 4, 9, 0) -> 187432960000 = 2^21 * 5^4 * 11 * 13 ,
(13, 4, 8, 1) -> 26142187500000 = 2^5 * 3^2 * 5^11 * 11 * 13^2 ,
(13, 4, 7, 2) -> 686929351680000 = 2^13 * 3^8 * 5^4 * 11^2 * 13^2 ,
(13, 4, 6, 3) -> 5249027784000000 = 2^9 * 3 * 5^6 * 7^6 * 11 * 13^2 ,
(13, 4, 5, 4) -> 13988379525120000 = 2^18 * 3^8 * 5^4 * 7 * 11 * 13^2 ,
(13, 4, 4, 5) -> 13988379525120000 = 2^18 * 3^8 * 5^4 * 7 * 11 * 13^2 ,
(13, 4, 3, 6) -> 5249027784000000 = 2^9 * 3 * 5^6 * 7^6 * 11 * 13^2 ,
(13, 4, 2, 7) -> 686929351680000 = 2^13 * 3^8 * 5^4 * 11^2 * 13^2 ,
(13, 4, 1, 8) -> 26142187500000 = 2^5 * 3^2 * 5^11 * 11 * 13^2 ,
(13, 4, 0, 9) -> 187432960000 = 2^21 * 5^4 * 11 * 13 ,
(13, 3, 10, 0) -> 2043449694 = 2 * 3^10 * 11^3 * 13 ,
(13, 3, 9, 1) -> 884496138240 = 2^18 * 3 * 5 * 11^3 * 13^2 ,
(13, 3, 8, 2) -> 52192877343750 = 2 * 3^3 * 5^8 * 11^4 * 13^2 ,
(13, 3, 7, 3) -> 755622286848000 = 2^12 * 3^8 * 5^3 * 11^3 * 13^2 ,
(13, 3, 6, 4) -> 3472586188491420 = 2^2 * 3^8 * 5 * 7^6 * 11^3 * 13^2 ,
(13, 3, 5, 5) -> 5706061487013888 = 2^27 * 3^3 * 7 * 11^3 * 13^2 ,
(13, 3, 4, 6) -> 3472586188491420 = 2^2 * 3^8 * 5 * 7^6 * 11^3 * 13^2 ,
(13, 3, 3, 7) -> 755622286848000 = 2^12 * 3^8 * 5^3 * 11^3 * 13^2 ,
(13, 3, 2, 8) -> 52192877343750 = 2 * 3^3 * 5^8 * 11^4 * 13^2 ,
(13, 3, 1, 9) -> 884496138240 = 2^18 * 3 * 5 * 11^3 * 13^2 ,
(13, 3, 0, 10) -> 2043449694 = 2 * 3^10 * 11^3 * 13 ,
(13, 2, 11, 0) -> 1916928 = 2^14 * 3^2 * 13 ,
(13, 2, 10, 1) -> 5269060368 = 2^4 * 3^11 * 11 * 13^2 ,
(13, 2, 9, 2) -> 964904878080 = 2^20 * 3^2 * 5 * 11^2 * 13^2 ,
(13, 2, 8, 3) -> 31370625000000 = 2^6 * 3^3 * 5^10 * 11 * 13^2 ,
(13, 2, 7, 4) -> 273148089477120 = 2^11 * 3^15 * 5 * 11 * 13^2 ,
(13, 2, 6, 5) -> 774000640917504 = 2^17 * 3^3 * 7^6 * 11 * 13^2 ,
(13, 2, 5, 6) -> 774000640917504 = 2^17 * 3^3 * 7^6 * 11 * 13^2 ,
(13, 2, 4, 7) -> 273148089477120 = 2^11 * 3^15 * 5 * 11 * 13^2 ,
(13, 2, 3, 8) -> 31370625000000 = 2^6 * 3^3 * 5^10 * 11 * 13^2 ,
(13, 2, 2, 9) -> 964904878080 = 2^20 * 3^2 * 5 * 11^2 * 13^2 ,
(13, 2, 1, 10) -> 5269060368 = 2^4 * 3^11 * 11 * 13^2 ,
(13, 2, 0, 11) -> 1916928 = 2^14 * 3^2 * 13 ,
(13, 1, 12, 0) -> 13 = 13 ,
(13, 1, 11, 1) -> 2076672 = 2^12 * 3 * 13^2 ,
(13, 1, 10, 2) -> 2414986002 = 2 * 3^10 * 11^2 * 13^2 ,
(13, 1, 9, 3) -> 243662848000 = 2^20 * 5^3 * 11 * 13^2 ,
(13, 1, 8, 4) -> 4764413671875 = 3^8 * 5^8 * 11 * 13^2 ,
(13, 1, 7, 5) -> 25578751131648 = 2^21 * 3^8 * 11 * 13^2 ,
(13, 1, 6, 6) -> 44110204982844 = 2^2 * 3 * 7^11 * 11 * 13^2 ,
(13, 1, 5, 7) -> 25578751131648 = 2^21 * 3^8 * 11 * 13^2 ,
(13, 1, 4, 8) -> 4764413671875 = 3^8 * 5^8 * 11 * 13^2 ,
(13, 1, 3, 9) -> 243662848000 = 2^20 * 5^3 * 11 * 13^2 ,
(13, 1, 2, 10) -> 2414986002 = 2 * 3^10 * 11^2 * 13^2 ,
(13, 1, 1, 11) -> 2076672 = 2^12 * 3 * 13^2 ,
(13, 1, 0, 12) -> 13 = 13 ,
n=14
(14, 14, 0, 0) -> 1 = 1 ,
(14, 13, 1, 0) -> 745472 = 2^13 * 7 * 13 ,
(14, 13, 0, 1) -> 745472 = 2^13 * 7 * 13 ,
(14, 12, 2, 0) -> 2321334288 = 2^4 * 3^13 * 7 * 13 ,
(14, 12, 1, 1) -> 5416446672 = 2^4 * 3^12 * 7^2 * 13 ,
(14, 12, 0, 2) -> 2321334288 = 2^4 * 3^13 * 7 * 13 ,
(14, 11, 3, 0) -> 508018294784 = 2^22 * 7 * 11^3 * 13 ,
(14, 11, 2, 1) -> 2116043145216 = 2^25 * 3^2 * 7^2 * 11 * 13 ,
(14, 11, 1, 2) -> 2116043145216 = 2^25 * 3^2 * 7^2 * 11 * 13 ,
(14, 11, 0, 3) -> 508018294784 = 2^22 * 7 * 11^3 * 13 ,
(14, 10, 4, 0) -> 19550781250000 = 2^4 * 5^13 * 7 * 11 * 13 ,
(14, 10, 3, 1) -> 132476093750000 = 2^4 * 5^10 * 7^2 * 11^3 * 13 ,
(14, 10, 2, 2) -> 236486250000000 = 2^7 * 3^3 * 5^10 * 7^2 * 11 * 13 ,
(14, 10, 1, 3) -> 132476093750000 = 2^4 * 5^10 * 7^2 * 11^3 * 13 ,
(14, 10, 0, 4) -> 19550781250000 = 2^4 * 5^13 * 7 * 11 * 13 ,
(14, 9, 5, 0) -> 198557649658368 = 2^9 * 3^18 * 7 * 11 * 13 ,
(14, 9, 4, 1) -> 2118432476160000 = 2^13 * 3^10 * 5^4 * 7^2 * 11 * 13 ,
(14, 9, 3, 2) -> 6151927910768640 = 2^13 * 3^11 * 5 * 7^2 * 11^3 * 13 ,
(14, 9, 2, 3) -> 6151927910768640 = 2^13 * 3^11 * 5 * 7^2 * 11^3 * 13 ,
(14, 9, 1, 4) -> 2118432476160000 = 2^13 * 3^10 * 5^4 * 7^2 * 11 * 13 ,
(14, 9, 0, 5) -> 198557649658368 = 2^9 * 3^18 * 7 * 11 * 13 ,
(14, 8, 6, 0) -> 648308229144576 = 2^18 * 3 * 7^8 * 11 * 13 ,
(14, 8, 5, 1) -> 10903876479463968 = 2^5 * 3^10 * 7^9 * 11 * 13 ,
(14, 8, 4, 2) -> 49857688520640000 = 2^9 * 3^3 * 5^4 * 7^9 * 11 * 13 ,
(14, 8, 3, 3) -> 81107379736743360 = 2^6 * 3 * 5 * 7^9 * 11^5 * 13 ,
(14, 8, 2, 4) -> 49857688520640000 = 2^9 * 3^3 * 5^4 * 7^9 * 11 * 13 ,
(14, 8, 1, 5) -> 10903876479463968 = 2^5 * 3^10 * 7^9 * 11 * 13 ,
(14, 8, 0, 6) -> 648308229144576 = 2^18 * 3 * 7^8 * 11 * 13 ,
(14, 7, 7, 0) -> 740923690450944 = 2^21 * 3 * 7^7 * 11 * 13 ,
(14, 7, 6, 1) -> 20223729686544384 = 2^37 * 3 * 7^3 * 11 * 13 ,
(14, 7, 5, 2) -> 145775270295502848 = 2^24 * 3^11 * 7^3 * 11 * 13 ,
(14, 7, 4, 3) -> 373393446666240000 = 2^25 * 3 * 5^4 * 7^3 * 11^3 * 13 ,
(14, 7, 3, 4) -> 373393446666240000 = 2^25 * 3 * 5^4 * 7^3 * 11^3 * 13 ,
(14, 7, 2, 5) -> 145775270295502848 = 2^24 * 3^11 * 7^3 * 11 * 13 ,
(14, 7, 1, 6) -> 20223729686544384 = 2^37 * 3 * 7^3 * 11 * 13 ,
(14, 7, 0, 7) -> 740923690450944 = 2^21 * 3 * 7^7 * 11 * 13 ,
(14, 6, 8, 0) -> 297836474487552 = 2^8 * 3^19 * 7 * 11 * 13 ,
(14, 6, 7, 1) -> 14019269759310816 = 2^5 * 3^12 * 7^8 * 11 * 13 ,
(14, 6, 6, 2) -> 163997179082440704 = 2^21 * 3^13 * 7^3 * 11 * 13 ,
(14, 6, 5, 3) -> 662202171463760928 = 2^5 * 3^20 * 7^3 * 11^3 * 13 ,
(14, 6, 4, 4) -> 1042665984360000000 = 2^9 * 3^12 * 5^7 * 7^3 * 11 * 13 ,
(14, 6, 3, 5) -> 662202171463760928 = 2^5 * 3^20 * 7^3 * 11^3 * 13 ,
(14, 6, 2, 6) -> 163997179082440704 = 2^21 * 3^13 * 7^3 * 11 * 13 ,
(14, 6, 1, 7) -> 14019269759310816 = 2^5 * 3^12 * 7^8 * 11 * 13 ,
(14, 6, 0, 8) -> 297836474487552 = 2^8 * 3^19 * 7 * 11 * 13 ,
(14, 5, 9, 0) -> 39101562500000 = 2^5 * 5^13 * 7 * 11 * 13 ,
(14, 5, 8, 1) -> 3530720793600000 = 2^13 * 3^9 * 5^5 * 7^2 * 11 * 13 ,
(14, 5, 7, 2) -> 71225269315200000 = 2^10 * 3^3 * 5^5 * 7^8 * 11 * 13 ,
(14, 5, 6, 3) -> 466741808332800000 = 2^23 * 3 * 5^5 * 7^3 * 11^3 * 13 ,
(14, 5, 5, 4) -> 1158517760400000000 = 2^10 * 3^10 * 5^8 * 7^3 * 11 * 13 ,
(14, 5, 4, 5) -> 1158517760400000000 = 2^10 * 3^10 * 5^8 * 7^3 * 11 * 13 ,
(14, 5, 3, 6) -> 466741808332800000 = 2^23 * 3 * 5^5 * 7^3 * 11^3 * 13 ,
(14, 5, 2, 7) -> 71225269315200000 = 2^10 * 3^3 * 5^5 * 7^8 * 11 * 13 ,
(14, 5, 1, 8) -> 3530720793600000 = 2^13 * 3^9 * 5^5 * 7^2 * 11 * 13 ,
(14, 5, 0, 9) -> 39101562500000 = 2^5 * 5^13 * 7 * 11 * 13 ,
(14, 4, 10, 0) -> 1397050310656 = 2^20 * 7 * 11^4 * 13 ,
(14, 4, 9, 1) -> 291447406250000 = 2^4 * 5^9 * 7^2 * 11^4 * 13 ,
(14, 4, 8, 2) -> 11278534503075840 = 2^12 * 3^10 * 5 * 7^2 * 11^4 * 13 ,
(14, 4, 7, 3) -> 127454453872025280 = 2^6 * 3 * 5 * 7^8 * 11^6 * 13 ,
(14, 4, 6, 4) -> 513415989166080000 = 2^22 * 3 * 5^4 * 7^3 * 11^4 * 13 ,
(14, 4, 5, 5) -> 809358209566818912 = 2^5 * 3^18 * 7^3 * 11^4 * 13 ,
(14, 4, 4, 6) -> 513415989166080000 = 2^22 * 3 * 5^4 * 7^3 * 11^4 * 13 ,
(14, 4, 3, 7) -> 127454453872025280 = 2^6 * 3 * 5 * 7^8 * 11^6 * 13 ,
(14, 4, 2, 8) -> 11278534503075840 = 2^12 * 3^10 * 5 * 7^2 * 11^4 * 13 ,
(14, 4, 1, 9) -> 291447406250000 = 2^4 * 5^9 * 7^2 * 11^4 * 13 ,
(14, 4, 0, 10) -> 1397050310656 = 2^20 * 7 * 11^4 * 13 ,
(14, 3, 11, 0) -> 9285337152 = 2^6 * 3^13 * 7 * 13 ,
(14, 3, 10, 1) -> 6348129435648 = 2^25 * 3^3 * 7^2 * 11 * 13 ,
(14, 3, 9, 2) -> 567567000000000 = 2^9 * 3^4 * 5^9 * 7^2 * 11 * 13 ,
(14, 3, 8, 3) -> 12303855821537280 = 2^14 * 3^11 * 5 * 7^2 * 11^3 * 13 ,
(14, 3, 7, 4) -> 85470323178240000 = 2^11 * 3^4 * 5^4 * 7^8 * 11 * 13 ,
(14, 3, 6, 5) -> 218662905443254272 = 2^23 * 3^12 * 7^3 * 11 * 13 ,
(14, 3, 5, 6) -> 218662905443254272 = 2^23 * 3^12 * 7^3 * 11 * 13 ,
(14, 3, 4, 7) -> 85470323178240000 = 2^11 * 3^4 * 5^4 * 7^8 * 11 * 13 ,
(14, 3, 3, 8) -> 12303855821537280 = 2^14 * 3^11 * 5 * 7^2 * 11^3 * 13 ,
(14, 3, 2, 9) -> 567567000000000 = 2^9 * 3^4 * 5^9 * 7^2 * 11 * 13 ,
(14, 3, 1, 10) -> 6348129435648 = 2^25 * 3^3 * 7^2 * 11 * 13 ,
(14, 3, 0, 11) -> 9285337152 = 2^6 * 3^13 * 7 * 13 ,
(14, 2, 12, 0) -> 4845568 = 2^12 * 7 * 13^2 ,
(14, 2, 11, 1) -> 23471268912 = 2^4 * 3^11 * 7^2 * 13^2 ,
(14, 2, 10, 2) -> 6877140221952 = 2^23 * 3^2 * 7^2 * 11 * 13^2 ,
(14, 2, 9, 3) -> 344437843750000 = 2^4 * 5^9 * 7^2 * 11^3 * 13^2 ,
(14, 2, 8, 4) -> 4589937031680000 = 2^12 * 3^9 * 5^4 * 7^2 * 11 * 13^2 ,
(14, 2, 7, 5) -> 20250056319004512 = 2^5 * 3^10 * 7^8 * 11 * 13^2 ,
(14, 2, 6, 6) -> 32863560740634624 = 2^34 * 3 * 7^3 * 11 * 13^2 ,
(14, 2, 5, 7) -> 20 250 056 319 004 512 = 2^5 * 3^10 * 7^8 * 11 * 13^2 ,
(14, 2, 4, 8) -> 4589937031680000 = 2^12 * 3^9 * 5^4 * 7^2 * 11 * 13^2 ,
(14, 2, 3, 9) -> 344437843750000 = 2^4 * 5^9 * 7^2 * 11^3 * 13^2 ,
(14, 2, 2, 10) -> 6877140221952 = 2^23 * 3^2 * 7^2 * 11 * 13^2 ,
(14, 2, 1, 11) -> 23471268912 = 2^4 * 3^11 * 7^2 * 13^2 ,
(14, 2, 0, 12) -> 4845568 = 2^12 * 7 * 13^2 ,
(14, 1, 13, 0) -> 14 = 2 * 7 ,
(14, 1, 12, 1) -> 5218304 = 2^13 * 7^2 * 13 ,
(14, 1, 11, 2) -> 10832893344 = 2^5 * 3^12 * 7^2 * 13 ,
(14, 1, 10, 3) -> 1778064031744 = 2^21 * 7^2 * 11^3 * 13 ,
(14, 1, 9, 4) -> 54742187500000 = 2^5 * 5^12 * 7^2 * 11 * 13 ,
(14, 1, 8, 5) -> 463301182536192 = 2^9 * 3^17 * 7^2 * 11 * 13 ,
(14, 1, 7, 6) -> 1296616458289152 = 2^19 * 3 * 7^8 * 11 * 13 ,
(14, 1, 6, 7) -> 1296616458289152 = 2^19 * 3 * 7^8 * 11 * 13 ,
(14, 1, 5, 8) -> 463301182536192 = 2^9 * 3^17 * 7^2 * 11 * 13 ,
(14, 1, 4, 9) -> 54742187500000 = 2^5 * 5^12 * 7^2 * 11 * 13 ,
(14, 1, 3, 10) -> 1778064031744 = 2^21 * 7^2 * 11^3 * 13 ,
(14, 1, 2, 11) -> 10832893344 = 2^5 * 3^12 * 7^2 * 13 ,
(14, 1, 1, 12) -> 5218304 = 2^13 * 7^2 * 13 ,
(14, 1, 0, 13) -> 14 = 2 * 7 ,
====================================================================
Factorisations :
(r,b)=(1,1) n**2*(n-1)*(n-2)*3**(n-3)
(r,b)=(2,1) n**2*(n-1)*(n-2)**2*(n-3)*4**(n-4)/2
(r,b)=(3,1) n**2*(n-1)*(n-2)*(n-3)**3*(n-4)*5**(n-5)/6
(r,b)=(4,1) n**2*(n-1)*(n-2)*(n-3)*(n-4)**4*(n-5)*6**(n-6)/24
(r,b)=(5,1) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)**5*(n-6)*7**(n-7)/factorial(x[2])
(r,b)=(6,1) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)**6*(n-7)*8**(n-8)/factorial(x[2])
(r,b)=(7,1) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)**7*(n-8)*9**(n-9)/factorial(x[2])
(r,b)=(2,2) n**2*(n-1)*(n-2)**3*(n-3)*(n-4)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(3,2) n**2*(n-1)*(n-2)**2*(n-3)**3*(n-4)*(n-5)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(4,2) n**2*(n-1)*(n-2)**2*(n-3)*(n-4)**4*(n-5)*(n-6)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(5,2) n**2*(n-1)*(n-2)**2*(n-3)*(n-4)*(n-5)**5*(n-6)*(n-7)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(6,2) n**2*(n-1)*(n-2)**2*(n-3)*(n-4)*(n-5)*(n-6)**6*(n-7)*(n-8)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(7,2) n**2*(n-1)*(n-2)**2*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)**7*(n-8)*(n-9)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(3,3) n**2*(n-1)*(n-2)*(n-3)**5*(n-4)*(n-5)*(n-6)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(4,3) n**2*(n-1)*(n-2)*(n-3)**3*(n-4)**4*(n-5)*(n-6)*(n-7)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(5,3) n**2*(n-1)*(n-2)*(n-3)**3*(n-4)*(n-5)**5*(n-6)*(n-7)*(n-8)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(6,3) n**2*(n-1)*(n-2)*(n-3)**3*(n-4)*(n-5)*(n-6)**6*(n-7)*(n-8)*(n-9)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(7,3) n**2*(n-1)*(n-2)*(n-3)**3*(n-4)*(n-5)*(n-6)*(n-7)**7*(n-8)*(n-9)*(n-10)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(4,4) n**2*(n-1)*(n-2)*(n-3)*(n-4)**7*(n-5)*(n-6)*(n-7)*(n-8)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(5,4) n**2*(n-1)*(n-2)*(n-3)*(n-4)**4*(n-5)**5*(n-6)*(n-7)*(n-8)*(n-9)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(6,4) n**2*(n-1)*(n-2)*(n-3)*(n-4)**4*(n-5)*(n-6)**6*(n-7)*(n-8)*(n-9)*(n-10)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(7,4) n**2*(n-1)*(n-2)*(n-3)*(n-4)**4*(n-5)*(n-6)*(n-7)**7*(n-8)*(n-9)*(n-10)*(n-11)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(5,5) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)**9*(n-6)*(n-7)*(n-8)*(n-9)*(n-10)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(6,5) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)**5*(n-6)**6*(n-7)*(n-8)*(n-9)*(n-10)*(n-11)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(7,5) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)**5*(n-6)*(n-7)**7*(n-8)*(n-9)*(n-10)*(n-11)*(n-12)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])* factorial(x[3]))
(r,b)=(6,6) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)**11*(n-7)*(n-8)*(n-9)*(n-10)*(n-11)*(n-12)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
(r,b)=(7,6) n**2*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)**6*(n-7)**7*(n-8)*(n-9)*(n-10)*(n-11)*(n-12)*(n-13)*(x[2]+x[3]+1)**(x[1]-1)/(factorial(x[2])*factorial(x[3]))
Quelle formule ?
n!/r!v!b! * (n-r)^(r-1)*(n-b)^(b-1)*(n-v+1)^(v-1) *n
Pour rappel, pour 2 couleurs :
n!/r!v! * (n-r)^r*(n-v+1)^(v-1)
====================================================================
Sv=x*v + 1/2*x^2*v^2 + x^2*v*b + x^2*v*r + 1/6*x^3*v^3 + 2*x^3*v^2*b + 2*x^3*v^2*r + 1/2*x^3*v*b^2 + 3*x^3*v*b*r + 1/2*x^3*v*r^2 + 1/24*x^4*v^4 + 2*x^4*v^3*b + 2*x^4*v^3*r + 3*x^4*v^2*b^2 + 12*x^4*v^2*b*r + 3*x^4*v^2*r^2 + 1/6*x^4*v*b^3 + 4*x^4*v*b^2*r + 4*x^4*v*b*r^2 + 1/6*x^4*v*r^3 + 1/120*x^5*v^5 + 4/3*x^5*v^4*b + 4/3*x^5*v^4*r + 27/4*x^5*v^3*b^2 + 45/2*x^5*v^3*b*r + 27/4*x^5*v^3*r^2 + 8/3*x^5*v^2*b^3 + 30*x^5*v^2*b^2*r + 30*x^5*v^2*b*r^2 + 8/3*x^5*v^2*r^3 + 1/24*x^5*v*b^4 + 10/3*x^5*v*b^3*r + 45/4*x^5*v*b^2*r^2 + 10/3*x^5*v*b*r^3 + 1/24*x^5*v*r^4 + 1/720*x^6*v^6 + 2/3*x^6*v^5*b + 2/3*x^6*v^5*r + 9*x^6*v^4*b^2 + 27*x^6*v^4*b*r + 9*x^6*v^4*r^2 + 12*x^6*v^3*b^3 + 96*x^6*v^3*b^2*r + 96*x^6*v^3*b*r^2 + 12*x^6*v^3*r^3 + 5/3*x^6*v^2*b^4 + 45*x^6*v^2*b^3*r + 120*x^6*v^2*b^2*r^2 + 45*x^6*v^2*b*r^3 + 5/3*x^6*v^2*r^4 + 1/120*x^6*v*b^5 + 2*x^6*v*b^4*r + 18*x^6*v*b^3*r^2 + 18*x^6*v*b^2*r^3 + 2*x^6*v*b*r^4 + 1/120*x^6*v*r^5 + 1/5040*x^7*v^7 + 4/15*x^7*v^6*b + 4/15*x^7*v^6*r + 135/16*x^7*v^5*b^2 + 189/8*x^7*v^5*b*r + 135/16*x^7*v^5*r^2 + 256/9*x^7*v^4*b^3 + 560/3*x^7*v^4*b^2*r + 560/3*x^7*v^4*b*r^2 + 256/9*x^7*v^4*r^3 + 225/16*x^7*v^3*b^4 + 700/3*x^7*v^3*b^3*r + 4375/8*x^7*v^3*b^2*r^2 + 700/3*x^7*v^3*b*r^3 + 225/16*x^7*v^3*r^4 + 4/5*x^7*v^2*b^5 + 189/4*x^7*v^2*b^4*r + 280*x^7*v^2*b^3*r^2 + 280*x^7*v^2*b^2*r^3 + 189/4*x^7*v^2*b*r^4 + 4/5*x^7*v^2*r^5 + 1/720*x^7*v*b^6 + 14/15*x^7*v*b^5*r + 315/16*x^7*v*b^4*r^2 + 448/9*x^7*v*b^3*r^3 + 315/16*x^7*v*b^2*r^4 + 14/15*x^7*v*b*r^5 + 1/720*x^7*v*r^6 + 1/40320*x^8*v^8 + 4/45*x^8*v^7*b + 4/45*x^8*v^7*r + 243/40*x^8*v^6*b^2 + 81/5*x^8*v^6*b*r + 243/40*x^8*v^6*r^2 + 400/9*x^8*v^5*b^3 + 256*x^8*v^5*b^2*r + 256*x^8*v^5*b*r^2 + 400/9*x^8*v^5*r^3 + 500/9*x^8*v^4*b^4 + 6250/9*x^8*v^4*b^3*r + 1500*x^8*v^4*b^2*r^2 + 6250/9*x^8*v^4*b*r^3 + 500/9*x^8*v^4*r^4 + 243/20*x^8*v^3*b^5 + 384*x^8*v^3*b^4*r + 1800*x^8*v^3*b^3*r^2 + 1800*x^8*v^3*b^2*r^3 + 384*x^8*v^3*b*r^4 + 243/20*x^8*v^3*r^5 + 14/45*x^8*v^2*b^6 + 189/5*x^8*v^2*b^5*r + 448*x^8*v^2*b^4*r^2 + 8750/9*x^8*v^2*b^3*r^3 + 448*x^8*v^2*b^2*r^4 + 189/5*x^8*v^2*b*r^5 + 14/45*x^8*v^2*r^6 + 1/5040*x^8*v*b^7 + 16/45*x^8*v*b^6*r + 81/5*x^8*v*b^5*r^2 + 800/9*x^8*v*b^4*r^3 + 800/9*x^8*v*b^3*r^4 + 81/5*x^8*v*b^2*r^5 + 16/45*x^8*v*b*r^6 + 1/5040*x^8*v*r^7 + 1/362880*x^9*v^9 + 8/315*x^9*v^8*b + 8/315*x^9*v^8*r + 567/160*x^9*v^7*b^2 + 729/80*x^9*v^7*b*r + 567/160*x^9*v^7*r^2 + 256/5*x^9*v^6*b^3 + 1344/5*x^9*v^6*b^2*r + 1344/5*x^9*v^6*b*r^2 + 256/5*x^9*v^6*r^3 + 78125/576*x^9*v^5*b^4 + 5625/4*x^9*v^5*b^3*r + 91875/32*x^9*v^5*b^2*r^2 + 5625/4*x^9*v^5*b*r^3 + 78125/576*x^9*v^5*r^4 + 384/5*x^9*v^4*b^5 + 3375/2*x^9*v^4*b^4*r + 6804*x^9*v^4*b^3*r^2 + 6804*x^9*v^4*b^2*r^3 + 3375/2*x^9*v^4*b*r^4 + 384/5*x^9*v^4*r^5 + 1323/160*x^9*v^3*b^6 + 2352/5*x^9*v^3*b^5*r + 128625/32*x^9*v^3*b^4*r^2 + 7938*x^9*v^3*b^3*r^3 + 128625/32*x^9*v^3*b^2*r^4 + 2352/5*x^9*v^3*b*r^5 + 1323/160*x^9*v^3*r^6 + 32/315*x^9*v^2*b^7 + 243/10*x^9*v^2*b^6*r + 2688/5*x^9*v^2*b^5*r^2 + 2250*x^9*v^2*b^4*r^3 + 2250*x^9*v^2*b^3*r^4 + 2688/5*x^9*v^2*b^2*r^5 + 243/10*x^9*v^2*b*r^6 + 32/315*x^9*v^2*r^7 + 1/40320*x^9*v*b^8 + 4/35*x^9*v*b^7*r + 1701/160*x^9*v*b^6*r^2 + 576/5*x^9*v*b^5*r^3 + 15625/64*x^9*v*b^4*r^4 + 576/5*x^9*v*b^3*r^5 + 1701/160*x^9*v*b^2*r^6 + 4/35*x^9*v*b*r^7 + 1/40320*x^9*v*r^8 + 1/3628800*x^10*v^10 + 2/315*x^10*v^9*b + 2/315*x^10*v^9*r + 243/140*x^10*v^8*b^2 + 243/56*x^10*v^8*b*r + 243/140*x^10*v^8*r^2 + 6272/135*x^10*v^7*b^3 + 2048/9*x^10*v^7*b^2*r + 2048/9*x^10*v^7*b*r^2 + 6272/135*x^10*v^7*r^3 + 1875/8*x^10*v^6*b^4 + 153125/72*x^10*v^6*b^3*r + 12500/3*x^10*v^6*b^2*r^2 + 153125/72*x^10*v^6*b*r^3 + 1875/8*x^10*v^6*r^4 + 1125/4*x^10*v^5*b^5 + 4860*x^10*v^5*b^4*r + 17640*x^10*v^5*b^3*r^2 + 17640*x^10*v^5*b^2*r^3 + 4860*x^10*v^5*b*r^4 + 1125/4*x^10*v^5*r^5 + 10976/135*x^10*v^4*b^6 + 214375/72*x^10*v^4*b^5*r + 20580*x^10*v^4*b^4*r^2 + 4117715/108*x^10*v^4*b^3*r^3 + 20580*x^10*v^4*b^2*r^4 + 214375/72*x^10*v^4*b*r^5 + 10976/135*x^10*v^4*r^6 + 162/35*x^10*v^3*b^7 + 4096/9*x^10*v^3*b^6*r + 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S=x*(v+b+r) + 1/2*x^2*(v^2 + 6*v*b + 6*v*r+b^2 + 6*b*r + r^2 )+ 1/6*x^3*(v^3 + 24*v^2*b + 24*v^2*r + 24*v*b^2 + 96*v*b*r + 24*v*r^2 + b^3 + 24*b^2*r + 24*b*r^2 + r^3) + 1/24*x^4*v^4 + 10/3*x^4*v^3*b + 10/3*x^4*v^3*r + 45/4*x^4*v^2*b^2 + 75/2*x^4*v^2*b*r + 45/4*x^4*v^2*r^2 + 10/3*x^4*v*b^3 + 75/2*x^4*v*b^2*r + 75/2*x^4*v*b*r^2 + 10/3*x^4*v*r^3 + 1/24*x^4*b^4 + 10/3*x^4*b^3*r + 45/4*x^4*b^2*r^2 + 10/3*x^4*b*r^3 + 1/24*x^4*r^4 + 1/120*x^5*v^5 + 2*x^5*v^4*b + 2*x^5*v^4*r + 18*x^5*v^3*b^2 + 54*x^5*v^3*b*r + 18*x^5*v^3*r^2 + 18*x^5*v^2*b^3 + 144*x^5*v^2*b^2*r + 144*x^5*v^2*b*r^2 + 18*x^5*v^2*r^3 + 2*x^5*v*b^4 + 54*x^5*v*b^3*r + 144*x^5*v*b^2*r^2 + 54*x^5*v*b*r^3 + 2*x^5*v*r^4 + 1/120*x^5*b^5 + 2*x^5*b^4*r + 18*x^5*b^3*r^2 + 18*x^5*b^2*r^3 + 2*x^5*b*r^4 + 1/120*x^5*r^5 + 1/720*x^6*v^6 + 14/15*x^6*v^5*b + 14/15*x^6*v^5*r + 315/16*x^6*v^4*b^2 + 441/8*x^6*v^4*b*r + 315/16*x^6*v^4*r^2 + 448/9*x^6*v^3*b^3 + 980/3*x^6*v^3*b^2*r + 980/3*x^6*v^3*b*r^2 + 448/9*x^6*v^3*r^3 + 315/16*x^6*v^2*b^4 + 980/3*x^6*v^2*b^3*r + 6125/8*x^6*v^2*b^2*r^2 + 980/3*x^6*v^2*b*r^3 + 315/16*x^6*v^2*r^4 + 14/15*x^6*v*b^5 + 441/8*x^6*v*b^4*r + 980/3*x^6*v*b^3*r^2 + 980/3*x^6*v*b^2*r^3 + 441/8*x^6*v*b*r^4 + 14/15*x^6*v*r^5 + 1/720*x^6*b^6 + 14/15*x^6*b^5*r + 315/16*x^6*b^4*r^2 + 448/9*x^6*b^3*r^3 + 315/16*x^6*b^2*r^4 + 14/15*x^6*b*r^5 + 1/720*x^6*r^6 + 1/5040*x^7*v^7 + 16/45*x^7*v^6*b + 16/45*x^7*v^6*r + 81/5*x^7*v^5*b^2 + 216/5*x^7*v^5*b*r + 81/5*x^7*v^5*r^2 + 800/9*x^7*v^4*b^3 + 512*x^7*v^4*b^2*r + 512*x^7*v^4*b*r^2 + 800/9*x^7*v^4*r^3 + 800/9*x^7*v^3*b^4 + 10000/9*x^7*v^3*b^3*r + 2400*x^7*v^3*b^2*r^2 + 10000/9*x^7*v^3*b*r^3 + 800/9*x^7*v^3*r^4 + 81/5*x^7*v^2*b^5 + 512*x^7*v^2*b^4*r + 2400*x^7*v^2*b^3*r^2 + 2400*x^7*v^2*b^2*r^3 + 512*x^7*v^2*b*r^4 + 81/5*x^7*v^2*r^5 + 16/45*x^7*v*b^6 + 216/5*x^7*v*b^5*r + 512*x^7*v*b^4*r^2 + 10000/9*x^7*v*b^3*r^3 + 512*x^7*v*b^2*r^4 + 216/5*x^7*v*b*r^5 + 16/45*x^7*v*r^6 + 1/5040*x^7*b^7 + 16/45*x^7*b^6*r + 81/5*x^7*b^5*r^2 + 800/9*x^7*b^4*r^3 + 800/9*x^7*b^3*r^4 + 81/5*x^7*b^2*r^5 + 16/45*x^7*b*r^6 + 1/5040*x^7*r^7 + 1/40320*x^8*v^8 + 4/35*x^8*v^7*b + 4/35*x^8*v^7*r + 1701/160*x^8*v^6*b^2 + 2187/80*x^8*v^6*b*r + 1701/160*x^8*v^6*r^2 + 576/5*x^8*v^5*b^3 + 3024/5*x^8*v^5*b^2*r + 3024/5*x^8*v^5*b*r^2 + 576/5*x^8*v^5*r^3 + 15625/64*x^8*v^4*b^4 + 10125/4*x^8*v^4*b^3*r + 165375/32*x^8*v^4*b^2*r^2 + 10125/4*x^8*v^4*b*r^3 + 15625/64*x^8*v^4*r^4 + 576/5*x^8*v^3*b^5 + 10125/4*x^8*v^3*b^4*r + 10206*x^8*v^3*b^3*r^2 + 10206*x^8*v^3*b^2*r^3 + 10125/4*x^8*v^3*b*r^4 + 576/5*x^8*v^3*r^5 + 1701/160*x^8*v^2*b^6 + 3024/5*x^8*v^2*b^5*r + 165375/32*x^8*v^2*b^4*r^2 + 10206*x^8*v^2*b^3*r^3 + 165375/32*x^8*v^2*b^2*r^4 + 3024/5*x^8*v^2*b*r^5 + 1701/160*x^8*v^2*r^6 + 4/35*x^8*v*b^7 + 2187/80*x^8*v*b^6*r + 3024/5*x^8*v*b^5*r^2 + 10125/4*x^8*v*b^4*r^3 + 10125/4*x^8*v*b^3*r^4 + 3024/5*x^8*v*b^2*r^5 + 2187/80*x^8*v*b*r^6 + 4/35*x^8*v*r^7 + 1/40320*x^8*b^8 + 4/35*x^8*b^7*r + 1701/160*x^8*b^6*r^2 + 576/5*x^8*b^5*r^3 + 15625/64*x^8*b^4*r^4 + 576/5*x^8*b^3*r^5 + 1701/160*x^8*b^2*r^6 + 4/35*x^8*b*r^7 + 1/40320*x^8*r^8 + 1/362880*x^9*v^9 + 2/63*x^9*v^8*b + 2/63*x^9*v^8*r + 81/14*x^9*v^7*b^2 + 405/28*x^9*v^7*b*r + 81/14*x^9*v^7*r^2 + 3136/27*x^9*v^6*b^3 + 5120/9*x^9*v^6*b^2*r + 5120/9*x^9*v^6*b*r^2 + 3136/27*x^9*v^6*r^3 + 1875/4*x^9*v^5*b^4 + 153125/36*x^9*v^5*b^3*r + 25000/3*x^9*v^5*b^2*r^2 + 153125/36*x^9*v^5*b*r^3 + 1875/4*x^9*v^5*r^4 + 1875/4*x^9*v^4*b^5 + 8100*x^9*v^4*b^4*r + 29400*x^9*v^4*b^3*r^2 + 29400*x^9*v^4*b^2*r^3 + 8100*x^9*v^4*b*r^4 + 1875/4*x^9*v^4*r^5 + 3136/27*x^9*v^3*b^6 + 153125/36*x^9*v^3*b^5*r + 29400*x^9*v^3*b^4*r^2 + 2941225/54*x^9*v^3*b^3*r^3 + 29400*x^9*v^3*b^2*r^4 + 153125/36*x^9*v^3*b*r^5 + 3136/27*x^9*v^3*r^6 + 81/14*x^9*v^2*b^7 + 5120/9*x^9*v^2*b^6*r + 25000/3*x^9*v^2*b^5*r^2 + 29400*x^9*v^2*b^4*r^3 + 29400*x^9*v^2*b^3*r^4 + 25000/3*x^9*v^2*b^2*r^5 + 5120/9*x^9*v^2*b*r^6 + 81/14*x^9*v^2*r^7 + 2/63*x^9*v*b^8 + 405/28*x^9*v*b^7*r + 5120/9*x^9*v*b^6*r^2 + 153125/36*x^9*v*b^5*r^3 + 8100*x^9*v*b^4*r^4 + 153125/36*x^9*v*b^3*r^5 + 5120/9*x^9*v*b^2*r^6 + 405/28*x^9*v*b*r^7 + 2/63*x^9*v*r^8 + 1/362880*x^9*b^9 + 2/63*x^9*b^8*r + 81/14*x^9*b^7*r^2 + 3136/27*x^9*b^6*r^3 + 1875/4*x^9*b^5*r^4 + 1875/4*x^9*b^4*r^5 + 3136/27*x^9*b^3*r^6 + 81/14*x^9*b^2*r^7 + 2/63*x^9*b*r^8 + 1/362880*x^9*r^9
=============================
== With yellow (j) edges ! ==
=============================
n=1
(1, 1, 0, 0, 0) -> 1 = 1 ,
n=2
(2, 2, 0, 0, 0) -> 1 = 1 ,
(2, 1, 1, 0, 0) -> 2 = 2 ,
(2, 1, 0, 1, 0) -> 2 = 2 ,
(2, 1, 0, 0, 1) -> 2 = 2 ,
n=3
(3, 3, 0, 0, 0) -> 1 = 1 ,
(3, 2, 1, 0, 0) -> 12 = 2^2 * 3 ,
(3, 2, 0, 1, 0) -> 12 = 2^2 * 3 ,
(3, 2, 0, 0, 1) -> 12 = 2^2 * 3 ,
(3, 1, 2, 0, 0) -> 3 = 3 ,
(3, 1, 1, 1, 0) -> 18 = 2 * 3^2 ,
(3, 1, 1, 0, 1) -> 18 = 2 * 3^2 ,
(3, 1, 0, 2, 0) -> 3 = 3 ,
(3, 1, 0, 1, 1) -> 18 = 2 * 3^2 ,
(3, 1, 0, 0, 2) -> 3 = 3 ,
n=4
(4, 4, 0, 0, 0) -> 1 = 1 ,
(4, 3, 1, 0, 0) -> 48 = 2^4 * 3 ,
(4, 3, 0, 1, 0) -> 48 = 2^4 * 3 ,
(4, 3, 0, 0, 1) -> 48 = 2^4 * 3 ,
(4, 2, 2, 0, 0) -> 72 = 2^3 * 3^2 ,
(4, 2, 1, 1, 0) -> 288 = 2^5 * 3^2 ,
(4, 2, 1, 0, 1) -> 288 = 2^5 * 3^2 ,
(4, 2, 0, 2, 0) -> 72 = 2^3 * 3^2 ,
(4, 2, 0, 1, 1) -> 288 = 2^5 * 3^2 ,
(4, 2, 0, 0, 2) -> 72 = 2^3 * 3^2 ,
(4, 1, 3, 0, 0) -> 4 = 2^2 ,
(4, 1, 2, 1, 0) -> 96 = 2^5 * 3 ,
(4, 1, 2, 0, 1) -> 96 = 2^5 * 3 ,
(4, 1, 1, 2, 0) -> 96 = 2^5 * 3 ,
(4, 1, 1, 1, 1) -> 384 = 2^7 * 3 ,
(4, 1, 1, 0, 2) -> 96 = 2^5 * 3 ,
(4, 1, 0, 3, 0) -> 4 = 2^2 ,
(4, 1, 0, 2, 1) -> 96 = 2^5 * 3 ,
(4, 1, 0, 1, 2) -> 96 = 2^5 * 3 ,
(4, 1, 0, 0, 3) -> 4 = 2^2 ,
n=5
(5, 5, 0, 0, 0) -> 1 = 1 ,
(5, 4, 1, 0, 0) -> 160 = 2^5 * 5 ,
(5, 4, 0, 1, 0) -> 160 = 2^5 * 5 ,
(5, 4, 0, 0, 1) -> 160 = 2^5 * 5 ,
(5, 3, 2, 0, 0) -> 810 = 2 * 3^4 * 5 ,
(5, 3, 1, 1, 0) -> 2700 = 2^2 * 3^3 * 5^2 ,
(5, 3, 1, 0, 1) -> 2700 = 2^2 * 3^3 * 5^2 ,
(5, 3, 0, 2, 0) -> 810 = 2 * 3^4 * 5 ,
(5, 3, 0, 1, 1) -> 2700 = 2^2 * 3^3 * 5^2 ,
(5, 3, 0, 0, 2) -> 810 = 2 * 3^4 * 5 ,
(5, 2, 3, 0, 0) -> 320 = 2^6 * 5 ,
(5, 2, 2, 1, 0) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 2, 0, 1) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 1, 2, 0) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 1, 1, 1) -> 12000 = 2^5 * 3 * 5^3 ,
(5, 2, 1, 0, 2) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 0, 3, 0) -> 320 = 2^6 * 5 ,
(5, 2, 0, 2, 1) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 0, 1, 2) -> 3600 = 2^4 * 3^2 * 5^2 ,
(5, 2, 0, 0, 3) -> 320 = 2^6 * 5 ,
(5, 1, 4, 0, 0) -> 5 = 5 ,
(5, 1, 3, 1, 0) -> 400 = 2^4 * 5^2 ,
(5, 1, 3, 0, 1) -> 400 = 2^4 * 5^2 ,
(5, 1, 2, 2, 0) -> 1350 = 2 * 3^3 * 5^2 ,
(5, 1, 2, 1, 1) -> 4500 = 2^2 * 3^2 * 5^3 ,
(5, 1, 2, 0, 2) -> 1350 = 2 * 3^3 * 5^2 ,
(5, 1, 1, 3, 0) -> 400 = 2^4 * 5^2 ,
(5, 1, 1, 2, 1) -> 4500 = 2^2 * 3^2 * 5^3 ,
(5, 1, 1, 1, 2) -> 4500 = 2^2 * 3^2 * 5^3 ,
(5, 1, 1, 0, 3) -> 400 = 2^4 * 5^2 ,
(5, 1, 0, 4, 0) -> 5 = 5 ,
(5, 1, 0, 3, 1) -> 400 = 2^4 * 5^2 ,
(5, 1, 0, 2, 2) -> 1350 = 2 * 3^3 * 5^2 ,
(5, 1, 0, 1, 3) -> 400 = 2^4 * 5^2 ,
(5, 1, 0, 0, 4) -> 5 = 5 ,
n=6
(6, 6, 0, 0, 0) -> 1 = 1 ,
(6, 5, 1, 0, 0) -> 480 = 2^5 * 3 * 5 ,
(6, 5, 0, 1, 0) -> 480 = 2^5 * 3 * 5 ,
(6, 5, 0, 0, 1) -> 480 = 2^5 * 3 * 5 ,
(6, 4, 2, 0, 0) -> 6480 = 2^4 * 3^4 * 5 ,
(6, 4, 1, 1, 0) -> 19440 = 2^4 * 3^5 * 5 ,
(6, 4, 1, 0, 1) -> 19440 = 2^4 * 3^5 * 5 ,
(6, 4, 0, 2, 0) -> 6480 = 2^4 * 3^4 * 5 ,
(6, 4, 0, 1, 1) -> 19440 = 2^4 * 3^5 * 5 ,
(6, 4, 0, 0, 2) -> 6480 = 2^4 * 3^4 * 5 ,
(6, 3, 3, 0, 0) -> 8640 = 2^6 * 3^3 * 5 ,
(6, 3, 2, 1, 0) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 2, 0, 1) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 1, 2, 0) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 1, 1, 1) -> 207360 = 2^9 * 3^4 * 5 ,
(6, 3, 1, 0, 2) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 0, 3, 0) -> 8640 = 2^6 * 3^3 * 5 ,
(6, 3, 0, 2, 1) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 0, 1, 2) -> 69120 = 2^9 * 3^3 * 5 ,
(6, 3, 0, 0, 3) -> 8640 = 2^6 * 3^3 * 5 ,
(6, 2, 4, 0, 0) -> 1200 = 2^4 * 3 * 5^2 ,
(6, 2, 3, 1, 0) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 3, 0, 1) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 2, 2, 0) -> 86400 = 2^7 * 3^3 * 5^2 ,
(6, 2, 2, 1, 1) -> 259200 = 2^7 * 3^4 * 5^2 ,
(6, 2, 2, 0, 2) -> 86400 = 2^7 * 3^3 * 5^2 ,
(6, 2, 1, 3, 0) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 1, 2, 1) -> 259200 = 2^7 * 3^4 * 5^2 ,
(6, 2, 1, 1, 2) -> 259200 = 2^7 * 3^4 * 5^2 ,
(6, 2, 1, 0, 3) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 0, 4, 0) -> 1200 = 2^4 * 3 * 5^2 ,
(6, 2, 0, 3, 1) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 0, 2, 2) -> 86400 = 2^7 * 3^3 * 5^2 ,
(6, 2, 0, 1, 3) -> 32400 = 2^4 * 3^4 * 5^2 ,
(6, 2, 0, 0, 4) -> 1200 = 2^4 * 3 * 5^2 ,
(6, 1, 5, 0, 0) -> 6 = 2 * 3 ,
(6, 1, 4, 1, 0) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 4, 0, 1) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 3, 2, 0) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 3, 1, 1) -> 38880 = 2^5 * 3^5 * 5 ,
(6, 1, 3, 0, 2) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 2, 3, 0) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 2, 2, 1) -> 103680 = 2^8 * 3^4 * 5 ,
(6, 1, 2, 1, 2) -> 103680 = 2^8 * 3^4 * 5 ,
(6, 1, 2, 0, 3) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 1, 4, 0) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 1, 3, 1) -> 38880 = 2^5 * 3^5 * 5 ,
(6, 1, 1, 2, 2) -> 103680 = 2^8 * 3^4 * 5 ,
(6, 1, 1, 1, 3) -> 38880 = 2^5 * 3^5 * 5 ,
(6, 1, 1, 0, 4) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 0, 5, 0) -> 6 = 2 * 3 ,
(6, 1, 0, 4, 1) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 0, 3, 2) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 0, 2, 3) -> 12960 = 2^5 * 3^4 * 5 ,
(6, 1, 0, 1, 4) -> 1440 = 2^5 * 3^2 * 5 ,
(6, 1, 0, 0, 5) -> 6 = 2 * 3 ,
==============================================================================
Sv=x*v + 1/2*x^2*v^2 + x^2*v*b + x^2*v*r + x^2*v*j + 1/6*x^3*v^3 + 2*x^3*v^2*b + 2*x^3*v^2*r + 2*x^3*v^2*j + 1/2*x^3*v*b^2 + 3*x^3*v*b*r + 3*x^3*v*b*j + 1/2*x^3*v*r^2 + 3*x^3*v*r*j + 1/2*x^3*v*j^2 + 1/24*x^4*v^4 + 2*x^4*v^3*b + 2*x^4*v^3*r + 2*x^4*v^3*j + 3*x^4*v^2*b^2 + 12*x^4*v^2*b*r + 12*x^4*v^2*b*j + 3*x^4*v^2*r^2 + 12*x^4*v^2*r*j + 3*x^4*v^2*j^2 + 1/6*x^4*v*b^3 + 4*x^4*v*b^2*r + 4*x^4*v*b^2*j + 4*x^4*v*b*r^2 + 16*x^4*v*b*r*j + 4*x^4*v*b*j^2 + 1/6*x^4*v*r^3 + 4*x^4*v*r^2*j + 4*x^4*v*r*j^2 + 1/6*x^4*v*j^3 + 1/120*x^5*v^5 + 4/3*x^5*v^4*b + 4/3*x^5*v^4*r + 4/3*x^5*v^4*j + 27/4*x^5*v^3*b^2 + 45/2*x^5*v^3*b*r + 45/2*x^5*v^3*b*j + 27/4*x^5*v^3*r^2 + 45/2*x^5*v^3*r*j + 27/4*x^5*v^3*j^2 + 8/3*x^5*v^2*b^3 + 30*x^5*v^2*b^2*r + 30*x^5*v^2*b^2*j + 30*x^5*v^2*b*r^2 + 100*x^5*v^2*b*r*j + 30*x^5*v^2*b*j^2 + 8/3*x^5*v^2*r^3 + 30*x^5*v^2*r^2*j + 30*x^5*v^2*r*j^2 + 8/3*x^5*v^2*j^3 + 1/24*x^5*v*b^4 + 10/3*x^5*v*b^3*r + 10/3*x^5*v*b^3*j + 45/4*x^5*v*b^2*r^2 + 75/2*x^5*v*b^2*r*j + 45/4*x^5*v*b^2*j^2 + 10/3*x^5*v*b*r^3 + 75/2*x^5*v*b*r^2*j + 75/2*x^5*v*b*r*j^2 + 10/3*x^5*v*b*j^3 + 1/24*x^5*v*r^4 + 10/3*x^5*v*r^3*j + 45/4*x^5*v*r^2*j^2 + 10/3*x^5*v*r*j^3 + 1/24*x^5*v*j^4 + 1/720*x^6*v^6 + 2/3*x^6*v^5*b + 2/3*x^6*v^5*r + 2/3*x^6*v^5*j + 9*x^6*v^4*b^2 + 27*x^6*v^4*b*r + 27*x^6*v^4*b*j + 9*x^6*v^4*r^2 + 27*x^6*v^4*r*j + 9*x^6*v^4*j^2 + 12*x^6*v^3*b^3 + 96*x^6*v^3*b^2*r + 96*x^6*v^3*b^2*j + 96*x^6*v^3*b*r^2 + 288*x^6*v^3*b*r*j + 96*x^6*v^3*b*j^2 + 12*x^6*v^3*r^3 + 96*x^6*v^3*r^2*j + 96*x^6*v^3*r*j^2 + 12*x^6*v^3*j^3 + 5/3*x^6*v^2*b^4 + 45*x^6*v^2*b^3*r + 45*x^6*v^2*b^3*j + 120*x^6*v^2*b^2*r^2 + 360*x^6*v^2*b^2*r*j + 120*x^6*v^2*b^2*j^2 + 45*x^6*v^2*b*r^3 + 360*x^6*v^2*b*r^2*j + 360*x^6*v^2*b*r*j^2 + 45*x^6*v^2*b*j^3 + 5/3*x^6*v^2*r^4 + 45*x^6*v^2*r^3*j + 120*x^6*v^2*r^2*j^2 + 45*x^6*v^2*r*j^3 + 5/3*x^6*v^2*j^4 + 1/120*x^6*v*b^5 + 2*x^6*v*b^4*r + 2*x^6*v*b^4*j + 18*x^6*v*b^3*r^2 + 54*x^6*v*b^3*r*j + 18*x^6*v*b^3*j^2 + 18*x^6*v*b^2*r^3 + 144*x^6*v*b^2*r^2*j + 144*x^6*v*b^2*r*j^2 + 18*x^6*v*b^2*j^3 + 2*x^6*v*b*r^4 + 54*x^6*v*b*r^3*j + 144*x^6*v*b*r^2*j^2 + 54*x^6*v*b*r*j^3 + 2*x^6*v*b*j^4 + 1/120*x^6*v*r^5 + 2*x^6*v*r^4*j + 18*x^6*v*r^3*j^2 + 18*x^6*v*r^2*j^3 + 2*x^6*v*r*j^4 + 1/120*x^6*v*j^5+1/5040*x^7*v^7 + 4/15*x^7*v^6*b + 4/15*x^7*v^6*r + 4/15*x^7*v^6*j + 135/16*x^7*v^5*b^2 + 189/8*x^7*v^5*b*r + 189/8*x^7*v^5*b*j + 135/16*x^7*v^5*r^2 + 189/8*x^7*v^5*r*j + 135/16*x^7*v^5*j^2 + 256/9*x^7*v^4*b^3 + 560/3*x^7*v^4*b^2*r + 560/3*x^7*v^4*b^2*j + 560/3*x^7*v^4*b*r^2 + 1568/3*x^7*v^4*b*r*j + 560/3*x^7*v^4*b*j^2 + 256/9*x^7*v^4*r^3 + 560/3*x^7*v^4*r^2*j + 560/3*x^7*v^4*r*j^2 + 256/9*x^7*v^4*j^3 + 225/16*x^7*v^3*b^4 + 700/3*x^7*v^3*b^3*r + 700/3*x^7*v^3*b^3*j + 4375/8*x^7*v^3*b^2*r^2 + 6125/4*x^7*v^3*b^2*r*j + 4375/8*x^7*v^3*b^2*j^2 + 700/3*x^7*v^3*b*r^3 + 6125/4*x^7*v^3*b*r^2*j + 6125/4*x^7*v^3*b*r*j^2 + 700/3*x^7*v^3*b*j^3 + 225/16*x^7*v^3*r^4 + 700/3*x^7*v^3*r^3*j + 4375/8*x^7*v^3*r^2*j^2 + 700/3*x^7*v^3*r*j^3 + 225/16*x^7*v^3*j^4 + 4/5*x^7*v^2*b^5 + 189/4*x^7*v^2*b^4*r + 189/4*x^7*v^2*b^4*j + 280*x^7*v^2*b^3*r^2 + 784*x^7*v^2*b^3*r*j + 280*x^7*v^2*b^3*j^2 + 280*x^7*v^2*b^2*r^3 + 3675/2*x^7*v^2*b^2*r^2*j + 3675/2*x^7*v^2*b^2*r*j^2 + 280*x^7*v^2*b^2*j^3 + 189/4*x^7*v^2*b*r^4 + 784*x^7*v^2*b*r^3*j + 3675/2*x^7*v^2*b*r^2*j^2 + 784*x^7*v^2*b*r*j^3 + 189/4*x^7*v^2*b*j^4 + 4/5*x^7*v^2*r^5 + 189/4*x^7*v^2*r^4*j + 280*x^7*v^2*r^3*j^2 + 280*x^7*v^2*r^2*j^3 + 189/4*x^7*v^2*r*j^4 + 4/5*x^7*v^2*j^5 + 1/720*x^7*v*b^6 + 14/15*x^7*v*b^5*r + 14/15*x^7*v*b^5*j + 315/16*x^7*v*b^4*r^2 + 441/8*x^7*v*b^4*r*j + 315/16*x^7*v*b^4*j^2 + 448/9*x^7*v*b^3*r^3 + 980/3*x^7*v*b^3*r^2*j + 980/3*x^7*v*b^3*r*j^2 + 448/9*x^7*v*b^3*j^3 + 315/16*x^7*v*b^2*r^4 + 980/3*x^7*v*b^2*r^3*j + 6125/8*x^7*v*b^2*r^2*j^2 + 980/3*x^7*v*b^2*r*j^3 + 315/16*x^7*v*b^2*j^4 + 14/15*x^7*v*b*r^5 + 441/8*x^7*v*b*r^4*j + 980/3*x^7*v*b*r^3*j^2 + 980/3*x^7*v*b*r^2*j^3 + 441/8*x^7*v*b*r*j^4 + 14/15*x^7*v*b*j^5 + 1/720*x^7*v*r^6 + 14/15*x^7*v*r^5*j + 315/16*x^7*v*r^4*j^2 + 448/9*x^7*v*r^3*j^3 + 315/16*x^7*v*r^2*j^4 + 14/15*x^7*v*r*j^5 + 1/720*x^7*v*j^6
Sr=Sr=x*r + 1/2*x^2*r^2 + x^2*r*b + x^2*r*v + x^2*r*j + 1/6*x^3*r^3 + 2*x^3*r^2*b + 2*x^3*r^2*v + 2*x^3*r^2*j + 1/2*x^3*r*b^2 + 3*x^3*r*b*v + 3*x^3*r*b*j + 1/2*x^3*r*v^2 + 3*x^3*r*v*j + 1/2*x^3*r*j^2 + 1/24*x^4*r^4 + 2*x^4*r^3*b + 2*x^4*r^3*v + 2*x^4*r^3*j + 3*x^4*r^2*b^2 + 12*x^4*r^2*b*v + 12*x^4*r^2*b*j + 3*x^4*r^2*v^2 + 12*x^4*r^2*v*j + 3*x^4*r^2*j^2 + 1/6*x^4*r*b^3 + 4*x^4*r*b^2*v + 4*x^4*r*b^2*j + 4*x^4*r*b*v^2 + 16*x^4*r*b*v*j + 4*x^4*r*b*j^2 + 1/6*x^4*r*v^3 + 4*x^4*r*v^2*j + 4*x^4*r*v*j^2 + 1/6*x^4*r*j^3 + 1/120*x^5*r^5 + 4/3*x^5*r^4*b + 4/3*x^5*r^4*v + 4/3*x^5*r^4*j + 27/4*x^5*r^3*b^2 + 45/2*x^5*r^3*b*v + 45/2*x^5*r^3*b*j + 27/4*x^5*r^3*v^2 + 45/2*x^5*r^3*v*j + 27/4*x^5*r^3*j^2 + 8/3*x^5*r^2*b^3 + 30*x^5*r^2*b^2*v + 30*x^5*r^2*b^2*j + 30*x^5*r^2*b*v^2 + 100*x^5*r^2*b*v*j + 30*x^5*r^2*b*j^2 + 8/3*x^5*r^2*v^3 + 30*x^5*r^2*v^2*j + 30*x^5*r^2*v*j^2 + 8/3*x^5*r^2*j^3 + 1/24*x^5*r*b^4 + 10/3*x^5*r*b^3*v + 10/3*x^5*r*b^3*j + 45/4*x^5*r*b^2*v^2 + 75/2*x^5*r*b^2*v*j + 45/4*x^5*r*b^2*j^2 + 10/3*x^5*r*b*v^3 + 75/2*x^5*r*b*v^2*j + 75/2*x^5*r*b*v*j^2 + 10/3*x^5*r*b*j^3 + 1/24*x^5*r*v^4 + 10/3*x^5*r*v^3*j + 45/4*x^5*r*v^2*j^2 + 10/3*x^5*r*v*j^3 + 1/24*x^5*r*j^4 + 1/720*x^6*r^6 + 2/3*x^6*r^5*b + 2/3*x^6*r^5*v + 2/3*x^6*r^5*j + 9*x^6*r^4*b^2 + 27*x^6*r^4*b*v + 27*x^6*r^4*b*j + 9*x^6*r^4*v^2 + 27*x^6*r^4*v*j + 9*x^6*r^4*j^2 + 12*x^6*r^3*b^3 + 96*x^6*r^3*b^2*v + 96*x^6*r^3*b^2*j + 96*x^6*r^3*b*v^2 + 288*x^6*r^3*b*v*j + 96*x^6*r^3*b*j^2 + 12*x^6*r^3*v^3 + 96*x^6*r^3*v^2*j + 96*x^6*r^3*v*j^2 + 12*x^6*r^3*j^3 + 5/3*x^6*r^2*b^4 + 45*x^6*r^2*b^3*v + 45*x^6*r^2*b^3*j + 120*x^6*r^2*b^2*v^2 + 360*x^6*r^2*b^2*v*j + 120*x^6*r^2*b^2*j^2 + 45*x^6*r^2*b*v^3 + 360*x^6*r^2*b*v^2*j + 360*x^6*r^2*b*v*j^2 + 45*x^6*r^2*b*j^3 + 5/3*x^6*r^2*v^4 + 45*x^6*r^2*v^3*j + 120*x^6*r^2*v^2*j^2 + 45*x^6*r^2*v*j^3 + 5/3*x^6*r^2*j^4 + 1/120*x^6*r*b^5 + 2*x^6*r*b^4*v + 2*x^6*r*b^4*j + 18*x^6*r*b^3*v^2 + 54*x^6*r*b^3*v*j + 18*x^6*r*b^3*j^2 + 18*x^6*r*b^2*v^3 + 144*x^6*r*b^2*v^2*j + 144*x^6*r*b^2*v*j^2 + 18*x^6*r*b^2*j^3 + 2*x^6*r*b*v^4 + 54*x^6*r*b*v^3*j + 144*x^6*r*b*v^2*j^2 + 54*x^6*r*b*v*j^3 + 2*x^6*r*b*j^4 + 1/120*x^6*r*v^5 + 2*x^6*r*v^4*j + 18*x^6*r*v^3*j^2 + 18*x^6*r*v^2*j^3 + 2*x^6*r*v*j^4 + 1/120*x^6*r*j^5
Sj=x*j + 1/2*x^2*j^2 + x^2*j*r + x^2*j*v + x^2*j*b + 1/6*x^3*j^3 + 2*x^3*j^2*r + 2*x^3*j^2*v + 2*x^3*j^2*b + 1/2*x^3*j*r^2 + 3*x^3*j*r*v + 3*x^3*j*r*b + 1/2*x^3*j*v^2 + 3*x^3*j*v*b + 1/2*x^3*j*b^2 + 1/24*x^4*j^4 + 2*x^4*j^3*r + 2*x^4*j^3*v + 2*x^4*j^3*b + 3*x^4*j^2*r^2 + 12*x^4*j^2*r*v + 12*x^4*j^2*r*b + 3*x^4*j^2*v^2 + 12*x^4*j^2*v*b + 3*x^4*j^2*b^2 + 1/6*x^4*j*r^3 + 4*x^4*j*r^2*v + 4*x^4*j*r^2*b + 4*x^4*j*r*v^2 + 16*x^4*j*r*v*b + 4*x^4*j*r*b^2 + 1/6*x^4*j*v^3 + 4*x^4*j*v^2*b + 4*x^4*j*v*b^2 + 1/6*x^4*j*b^3 + 1/120*x^5*j^5 + 4/3*x^5*j^4*r + 4/3*x^5*j^4*v + 4/3*x^5*j^4*b + 27/4*x^5*j^3*r^2 + 45/2*x^5*j^3*r*v + 45/2*x^5*j^3*r*b + 27/4*x^5*j^3*v^2 + 45/2*x^5*j^3*v*b + 27/4*x^5*j^3*b^2 + 8/3*x^5*j^2*r^3 + 30*x^5*j^2*r^2*v + 30*x^5*j^2*r^2*b + 30*x^5*j^2*r*v^2 + 100*x^5*j^2*r*v*b + 30*x^5*j^2*r*b^2 + 8/3*x^5*j^2*v^3 + 30*x^5*j^2*v^2*b + 30*x^5*j^2*v*b^2 + 8/3*x^5*j^2*b^3 + 1/24*x^5*j*r^4 + 10/3*x^5*j*r^3*v + 10/3*x^5*j*r^3*b + 45/4*x^5*j*r^2*v^2 + 75/2*x^5*j*r^2*v*b + 45/4*x^5*j*r^2*b^2 + 10/3*x^5*j*r*v^3 + 75/2*x^5*j*r*v^2*b + 75/2*x^5*j*r*v*b^2 + 10/3*x^5*j*r*b^3 + 1/24*x^5*j*v^4 + 10/3*x^5*j*v^3*b + 45/4*x^5*j*v^2*b^2 + 10/3*x^5*j*v*b^3 + 1/24*x^5*j*b^4 + 1/720*x^6*j^6 + 2/3*x^6*j^5*r + 2/3*x^6*j^5*v + 2/3*x^6*j^5*b + 9*x^6*j^4*r^2 + 27*x^6*j^4*r*v + 27*x^6*j^4*r*b + 9*x^6*j^4*v^2 + 27*x^6*j^4*v*b + 9*x^6*j^4*b^2 + 12*x^6*j^3*r^3 + 96*x^6*j^3*r^2*v + 96*x^6*j^3*r^2*b + 96*x^6*j^3*r*v^2 + 288*x^6*j^3*r*v*b + 96*x^6*j^3*r*b^2 + 12*x^6*j^3*v^3 + 96*x^6*j^3*v^2*b + 96*x^6*j^3*v*b^2 + 12*x^6*j^3*b^3 + 5/3*x^6*j^2*r^4 + 45*x^6*j^2*r^3*v + 45*x^6*j^2*r^3*b + 120*x^6*j^2*r^2*v^2 + 360*x^6*j^2*r^2*v*b + 120*x^6*j^2*r^2*b^2 + 45*x^6*j^2*r*v^3 + 360*x^6*j^2*r*v^2*b + 360*x^6*j^2*r*v*b^2 + 45*x^6*j^2*r*b^3 + 5/3*x^6*j^2*v^4 + 45*x^6*j^2*v^3*b + 120*x^6*j^2*v^2*b^2 + 45*x^6*j^2*v*b^3 + 5/3*x^6*j^2*b^4 + 1/120*x^6*j*r^5 + 2*x^6*j*r^4*v + 2*x^6*j*r^4*b + 18*x^6*j*r^3*v^2 + 54*x^6*j*r^3*v*b + 18*x^6*j*r^3*b^2 + 18*x^6*j*r^2*v^3 + 144*x^6*j*r^2*v^2*b + 144*x^6*j*r^2*v*b^2 + 18*x^6*j*r^2*b^3 + 2*x^6*j*r*v^4 + 54*x^6*j*r*v^3*b + 144*x^6*j*r*v^2*b^2 + 54*x^6*j*r*v*b^3 + 2*x^6*j*r*b^4 + 1/120*x^6*j*v^5 + 2*x^6*j*v^4*b + 18*x^6*j*v^3*b^2 + 18*x^6*j*v^2*b^3 + 2*x^6*j*v*b^4 + 1/120*x^6*j*b^5
=======================================================
5 COLORS
b,r,v,j,p
Sv=x*v + 1/2*x^2*v^2 + x^2*v*j + x^2*v*b + x^2*v*r + x^2*v*p +1/6*x^3*v^3 + 2*x^3*v^2*j + 2*x^3*v^2*b + 2*x^3*v^2*r + 2*x^3*v^2*p + 1/2*x^3*v*j^2 + 3*x^3*v*j*b + 3*x^3*v*j*r + 3*x^3*v*j*p + 1/2*x^3*v*b^2 + 3*x^3*v*b*r + 3*x^3*v*b*p + 1/2*x^3*v*r^2 + 3*x^3*v*r*p + 1/2*x^3*v*p^2+1/24*x^4*v^4 + 2*x^4*v^3*r + 2*x^4*v^3*j + 2*x^4*v^3*p + 2*x^4*v^3*b + 3*x^4*v^2*r^2 + 12*x^4*v^2*r*j + 12*x^4*v^2*r*p + 12*x^4*v^2*r*b + 3*x^4*v^2*j^2 + 12*x^4*v^2*j*p + 12*x^4*v^2*j*b + 3*x^4*v^2*p^2 + 12*x^4*v^2*p*b + 3*x^4*v^2*b^2 + 1/6*x^4*v*r^3 + 4*x^4*v*r^2*j + 4*x^4*v*r^2*p + 4*x^4*v*r^2*b + 4*x^4*v*r*j^2 + 16*x^4*v*r*j*p + 16*x^4*v*r*j*b + 4*x^4*v*r*p^2 + 16*x^4*v*r*p*b + 4*x^4*v*r*b^2 + 1/6*x^4*v*j^3 + 4*x^4*v*j^2*p + 4*x^4*v*j^2*b + 4*x^4*v*j*p^2 + 16*x^4*v*j*p*b + 4*x^4*v*j*b^2 + 1/6*x^4*v*p^3 + 4*x^4*v*p^2*b + 4*x^4*v*p*b^2 + 1/6*x^4*v*b^3+1/120*x^5*v^5 + 4/3*x^5*v^4*j + 4/3*x^5*v^4*p + 4/3*x^5*v^4*b + 4/3*x^5*v^4*r + 27/4*x^5*v^3*j^2 + 45/2*x^5*v^3*j*p + 45/2*x^5*v^3*j*b + 45/2*x^5*v^3*j*r + 27/4*x^5*v^3*p^2 + 45/2*x^5*v^3*p*b + 45/2*x^5*v^3*p*r + 27/4*x^5*v^3*b^2 + 45/2*x^5*v^3*b*r + 27/4*x^5*v^3*r^2 + 8/3*x^5*v^2*j^3 + 30*x^5*v^2*j^2*p + 30*x^5*v^2*j^2*b + 30*x^5*v^2*j^2*r + 30*x^5*v^2*j*p^2 + 100*x^5*v^2*j*p*b + 100*x^5*v^2*j*p*r + 30*x^5*v^2*j*b^2 + 100*x^5*v^2*j*b*r + 30*x^5*v^2*j*r^2 + 8/3*x^5*v^2*p^3 + 30*x^5*v^2*p^2*b + 30*x^5*v^2*p^2*r + 30*x^5*v^2*p*b^2 + 100*x^5*v^2*p*b*r + 30*x^5*v^2*p*r^2 + 8/3*x^5*v^2*b^3 + 30*x^5*v^2*b^2*r + 30*x^5*v^2*b*r^2 + 8/3*x^5*v^2*r^3 + 1/24*x^5*v*j^4 + 10/3*x^5*v*j^3*p + 10/3*x^5*v*j^3*b + 10/3*x^5*v*j^3*r + 45/4*x^5*v*j^2*p^2 + 75/2*x^5*v*j^2*p*b + 75/2*x^5*v*j^2*p*r + 45/4*x^5*v*j^2*b^2 + 75/2*x^5*v*j^2*b*r + 45/4*x^5*v*j^2*r^2 + 10/3*x^5*v*j*p^3 + 75/2*x^5*v*j*p^2*b + 75/2*x^5*v*j*p^2*r + 75/2*x^5*v*j*p*b^2 + 125*x^5*v*j*p*b*r + 75/2*x^5*v*j*p*r^2 + 10/3*x^5*v*j*b^3 + 75/2*x^5*v*j*b^2*r + 75/2*x^5*v*j*b*r^2 + 10/3*x^5*v*j*r^3 + 1/24*x^5*v*p^4 + 10/3*x^5*v*p^3*b + 10/3*x^5*v*p^3*r + 45/4*x^5*v*p^2*b^2 + 75/2*x^5*v*p^2*b*r + 45/4*x^5*v*p^2*r^2 + 10/3*x^5*v*p*b^3 + 75/2*x^5*v*p*b^2*r + 75/2*x^5*v*p*b*r^2 + 10/3*x^5*v*p*r^3 + 1/24*x^5*v*b^4 + 10/3*x^5*v*b^3*r + 45/4*x^5*v*b^2*r^2 + 10/3*x^5*v*b*r^3 + 1/24*x^5*v*r^4 +1/720*x^6*v^6 + 2/3*x^6*v^5*r + 2/3*x^6*v^5*j + 2/3*x^6*v^5*p + 2/3*x^6*v^5*b + 9*x^6*v^4*r^2 + 27*x^6*v^4*r*j + 27*x^6*v^4*r*p + 27*x^6*v^4*r*b + 9*x^6*v^4*j^2 + 27*x^6*v^4*j*p + 27*x^6*v^4*j*b + 9*x^6*v^4*p^2 + 27*x^6*v^4*p*b + 9*x^6*v^4*b^2 + 12*x^6*v^3*r^3 + 96*x^6*v^3*r^2*j + 96*x^6*v^3*r^2*p + 96*x^6*v^3*r^2*b + 96*x^6*v^3*r*j^2 + 288*x^6*v^3*r*j*p + 288*x^6*v^3*r*j*b + 96*x^6*v^3*r*p^2 + 288*x^6*v^3*r*p*b + 96*x^6*v^3*r*b^2 + 12*x^6*v^3*j^3 + 96*x^6*v^3*j^2*p + 96*x^6*v^3*j^2*b + 96*x^6*v^3*j*p^2 + 288*x^6*v^3*j*p*b + 96*x^6*v^3*j*b^2 + 12*x^6*v^3*p^3 + 96*x^6*v^3*p^2*b + 96*x^6*v^3*p*b^2 + 12*x^6*v^3*b^3 + 5/3*x^6*v^2*r^4 + 45*x^6*v^2*r^3*j + 45*x^6*v^2*r^3*p + 45*x^6*v^2*r^3*b + 120*x^6*v^2*r^2*j^2 + 360*x^6*v^2*r^2*j*p + 360*x^6*v^2*r^2*j*b + 120*x^6*v^2*r^2*p^2 + 360*x^6*v^2*r^2*p*b + 120*x^6*v^2*r^2*b^2 + 45*x^6*v^2*r*j^3 + 360*x^6*v^2*r*j^2*p + 360*x^6*v^2*r*j^2*b + 360*x^6*v^2*r*j*p^2 + 1080*x^6*v^2*r*j*p*b + 360*x^6*v^2*r*j*b^2 + 45*x^6*v^2*r*p^3 + 360*x^6*v^2*r*p^2*b + 360*x^6*v^2*r*p*b^2 + 45*x^6*v^2*r*b^3 + 5/3*x^6*v^2*j^4 + 45*x^6*v^2*j^3*p + 45*x^6*v^2*j^3*b + 120*x^6*v^2*j^2*p^2 + 360*x^6*v^2*j^2*p*b + 120*x^6*v^2*j^2*b^2 + 45*x^6*v^2*j*p^3 + 360*x^6*v^2*j*p^2*b + 360*x^6*v^2*j*p*b^2 + 45*x^6*v^2*j*b^3 + 5/3*x^6*v^2*p^4 + 45*x^6*v^2*p^3*b + 120*x^6*v^2*p^2*b^2 + 45*x^6*v^2*p*b^3 + 5/3*x^6*v^2*b^4 + 1/120*x^6*v*r^5 + 2*x^6*v*r^4*j + 2*x^6*v*r^4*p + 2*x^6*v*r^4*b + 18*x^6*v*r^3*j^2 + 54*x^6*v*r^3*j*p + 54*x^6*v*r^3*j*b + 18*x^6*v*r^3*p^2 + 54*x^6*v*r^3*p*b + 18*x^6*v*r^3*b^2 + 18*x^6*v*r^2*j^3 + 144*x^6*v*r^2*j^2*p + 144*x^6*v*r^2*j^2*b + 144*x^6*v*r^2*j*p^2 + 432*x^6*v*r^2*j*p*b + 144*x^6*v*r^2*j*b^2 + 18*x^6*v*r^2*p^3 + 144*x^6*v*r^2*p^2*b + 144*x^6*v*r^2*p*b^2 + 18*x^6*v*r^2*b^3 + 2*x^6*v*r*j^4 + 54*x^6*v*r*j^3*p + 54*x^6*v*r*j^3*b + 144*x^6*v*r*j^2*p^2 + 432*x^6*v*r*j^2*p*b + 144*x^6*v*r*j^2*b^2 + 54*x^6*v*r*j*p^3 + 432*x^6*v*r*j*p^2*b + 432*x^6*v*r*j*p*b^2 + 54*x^6*v*r*j*b^3 + 2*x^6*v*r*p^4 + 54*x^6*v*r*p^3*b + 144*x^6*v*r*p^2*b^2 + 54*x^6*v*r*p*b^3 + 2*x^6*v*r*b^4 + 1/120*x^6*v*j^5 + 2*x^6*v*j^4*p + 2*x^6*v*j^4*b + 18*x^6*v*j^3*p^2 + 54*x^6*v*j^3*p*b + 18*x^6*v*j^3*b^2 + 18*x^6*v*j^2*p^3 + 144*x^6*v*j^2*p^2*b + 144*x^6*v*j^2*p*b^2 + 18*x^6*v*j^2*b^3 + 2*x^6*v*j*p^4 + 54*x^6*v*j*p^3*b + 144*x^6*v*j*p^2*b^2 + 54*x^6*v*j*p*b^3 + 2*x^6*v*j*b^4 + 1/120*x^6*v*p^5 + 2*x^6*v*p^4*b + 18*x^6*v*p^3*b^2 + 18*x^6*v*p^2*b^3 + 2*x^6*v*p*b^4 + 1/120*x^6*v*b^5 +1/5040*x^7*v^7 + 4/15*x^7*v^6*b + 4/15*x^7*v^6*r + 4/15*x^7*v^6*j + 4/15*x^7*v^6*p + 135/16*x^7*v^5*b^2 + 189/8*x^7*v^5*b*r + 189/8*x^7*v^5*b*j + 189/8*x^7*v^5*b*p + 135/16*x^7*v^5*r^2 + 189/8*x^7*v^5*r*j + 189/8*x^7*v^5*r*p + 135/16*x^7*v^5*j^2 + 189/8*x^7*v^5*j*p + 135/16*x^7*v^5*p^2 + 256/9*x^7*v^4*b^3 + 560/3*x^7*v^4*b^2*r + 560/3*x^7*v^4*b^2*j + 560/3*x^7*v^4*b^2*p + 560/3*x^7*v^4*b*r^2 + 1568/3*x^7*v^4*b*r*j + 1568/3*x^7*v^4*b*r*p + 560/3*x^7*v^4*b*j^2 + 1568/3*x^7*v^4*b*j*p + 560/3*x^7*v^4*b*p^2 + 256/9*x^7*v^4*r^3 + 560/3*x^7*v^4*r^2*j + 560/3*x^7*v^4*r^2*p + 560/3*x^7*v^4*r*j^2 + 1568/3*x^7*v^4*r*j*p + 560/3*x^7*v^4*r*p^2 + 256/9*x^7*v^4*j^3 + 560/3*x^7*v^4*j^2*p + 560/3*x^7*v^4*j*p^2 + 256/9*x^7*v^4*p^3 + 225/16*x^7*v^3*b^4 + 700/3*x^7*v^3*b^3*r + 700/3*x^7*v^3*b^3*j + 700/3*x^7*v^3*b^3*p + 4375/8*x^7*v^3*b^2*r^2 + 6125/4*x^7*v^3*b^2*r*j + 6125/4*x^7*v^3*b^2*r*p + 4375/8*x^7*v^3*b^2*j^2 + 6125/4*x^7*v^3*b^2*j*p + 4375/8*x^7*v^3*b^2*p^2 + 700/3*x^7*v^3*b*r^3 + 6125/4*x^7*v^3*b*r^2*j + 6125/4*x^7*v^3*b*r^2*p + 6125/4*x^7*v^3*b*r*j^2 + 8575/2*x^7*v^3*b*r*j*p + 6125/4*x^7*v^3*b*r*p^2 + 700/3*x^7*v^3*b*j^3 + 6125/4*x^7*v^3*b*j^2*p + 6125/4*x^7*v^3*b*j*p^2 + 700/3*x^7*v^3*b*p^3 + 225/16*x^7*v^3*r^4 + 700/3*x^7*v^3*r^3*j + 700/3*x^7*v^3*r^3*p + 4375/8*x^7*v^3*r^2*j^2 + 6125/4*x^7*v^3*r^2*j*p + 4375/8*x^7*v^3*r^2*p^2 + 700/3*x^7*v^3*r*j^3 + 6125/4*x^7*v^3*r*j^2*p + 6125/4*x^7*v^3*r*j*p^2 + 700/3*x^7*v^3*r*p^3 + 225/16*x^7*v^3*j^4 + 700/3*x^7*v^3*j^3*p + 4375/8*x^7*v^3*j^2*p^2 + 700/3*x^7*v^3*j*p^3 + 225/16*x^7*v^3*p^4 + 4/5*x^7*v^2*b^5 + 189/4*x^7*v^2*b^4*r + 189/4*x^7*v^2*b^4*j + 189/4*x^7*v^2*b^4*p + 280*x^7*v^2*b^3*r^2 + 784*x^7*v^2*b^3*r*j + 784*x^7*v^2*b^3*r*p + 280*x^7*v^2*b^3*j^2 + 784*x^7*v^2*b^3*j*p + 280*x^7*v^2*b^3*p^2 + 280*x^7*v^2*b^2*r^3 + 3675/2*x^7*v^2*b^2*r^2*j + 3675/2*x^7*v^2*b^2*r^2*p + 3675/2*x^7*v^2*b^2*r*j^2 + 5145*x^7*v^2*b^2*r*j*p + 3675/2*x^7*v^2*b^2*r*p^2 + 280*x^7*v^2*b^2*j^3 + 3675/2*x^7*v^2*b^2*j^2*p + 3675/2*x^7*v^2*b^2*j*p^2 + 280*x^7*v^2*b^2*p^3 + 189/4*x^7*v^2*b*r^4 + 784*x^7*v^2*b*r^3*j + 784*x^7*v^2*b*r^3*p + 3675/2*x^7*v^2*b*r^2*j^2 + 5145*x^7*v^2*b*r^2*j*p + 3675/2*x^7*v^2*b*r^2*p^2 + 784*x^7*v^2*b*r*j^3 + 5145*x^7*v^2*b*r*j^2*p + 5145*x^7*v^2*b*r*j*p^2 + 784*x^7*v^2*b*r*p^3 + 189/4*x^7*v^2*b*j^4 + 784*x^7*v^2*b*j^3*p + 3675/2*x^7*v^2*b*j^2*p^2 + 784*x^7*v^2*b*j*p^3 + 189/4*x^7*v^2*b*p^4 + 4/5*x^7*v^2*r^5 + 189/4*x^7*v^2*r^4*j + 189/4*x^7*v^2*r^4*p + 280*x^7*v^2*r^3*j^2 + 784*x^7*v^2*r^3*j*p + 280*x^7*v^2*r^3*p^2 + 280*x^7*v^2*r^2*j^3 + 3675/2*x^7*v^2*r^2*j^2*p + 3675/2*x^7*v^2*r^2*j*p^2 + 280*x^7*v^2*r^2*p^3 + 189/4*x^7*v^2*r*j^4 + 784*x^7*v^2*r*j^3*p + 3675/2*x^7*v^2*r*j^2*p^2 + 784*x^7*v^2*r*j*p^3 + 189/4*x^7*v^2*r*p^4 + 4/5*x^7*v^2*j^5 + 189/4*x^7*v^2*j^4*p + 280*x^7*v^2*j^3*p^2 + 280*x^7*v^2*j^2*p^3 + 189/4*x^7*v^2*j*p^4 + 4/5*x^7*v^2*p^5 + 1/720*x^7*v*b^6 + 14/15*x^7*v*b^5*r + 14/15*x^7*v*b^5*j + 14/15*x^7*v*b^5*p + 315/16*x^7*v*b^4*r^2 + 441/8*x^7*v*b^4*r*j + 441/8*x^7*v*b^4*r*p + 315/16*x^7*v*b^4*j^2 + 441/8*x^7*v*b^4*j*p + 315/16*x^7*v*b^4*p^2 + 448/9*x^7*v*b^3*r^3 + 980/3*x^7*v*b^3*r^2*j + 980/3*x^7*v*b^3*r^2*p + 980/3*x^7*v*b^3*r*j^2 + 2744/3*x^7*v*b^3*r*j*p + 980/3*x^7*v*b^3*r*p^2 + 448/9*x^7*v*b^3*j^3 + 980/3*x^7*v*b^3*j^2*p + 980/3*x^7*v*b^3*j*p^2 + 448/9*x^7*v*b^3*p^3 + 315/16*x^7*v*b^2*r^4 + 980/3*x^7*v*b^2*r^3*j + 980/3*x^7*v*b^2*r^3*p + 6125/8*x^7*v*b^2*r^2*j^2 + 8575/4*x^7*v*b^2*r^2*j*p + 6125/8*x^7*v*b^2*r^2*p^2 + 980/3*x^7*v*b^2*r*j^3 + 8575/4*x^7*v*b^2*r*j^2*p + 8575/4*x^7*v*b^2*r*j*p^2 + 980/3*x^7*v*b^2*r*p^3 + 315/16*x^7*v*b^2*j^4 + 980/3*x^7*v*b^2*j^3*p + 6125/8*x^7*v*b^2*j^2*p^2 + 980/3*x^7*v*b^2*j*p^3 + 315/16*x^7*v*b^2*p^4 + 14/15*x^7*v*b*r^5 + 441/8*x^7*v*b*r^4*j + 441/8*x^7*v*b*r^4*p + 980/3*x^7*v*b*r^3*j^2 + 2744/3*x^7*v*b*r^3*j*p + 980/3*x^7*v*b*r^3*p^2 + 980/3*x^7*v*b*r^2*j^3 + 8575/4*x^7*v*b*r^2*j^2*p + 8575/4*x^7*v*b*r^2*j*p^2 + 980/3*x^7*v*b*r^2*p^3 + 441/8*x^7*v*b*r*j^4 + 2744/3*x^7*v*b*r*j^3*p + 8575/4*x^7*v*b*r*j^2*p^2 + 2744/3*x^7*v*b*r*j*p^3 + 441/8*x^7*v*b*r*p^4 + 14/15*x^7*v*b*j^5 + 441/8*x^7*v*b*j^4*p + 980/3*x^7*v*b*j^3*p^2 + 980/3*x^7*v*b*j^2*p^3 + 441/8*x^7*v*b*j*p^4 + 14/15*x^7*v*b*p^5 + 1/720*x^7*v*r^6 + 14/15*x^7*v*r^5*j + 14/15*x^7*v*r^5*p + 315/16*x^7*v*r^4*j^2 + 441/8*x^7*v*r^4*j*p + 315/16*x^7*v*r^4*p^2 + 448/9*x^7*v*r^3*j^3 + 980/3*x^7*v*r^3*j^2*p + 980/3*x^7*v*r^3*j*p^2 + 448/9*x^7*v*r^3*p^3 + 315/16*x^7*v*r^2*j^4 + 980/3*x^7*v*r^2*j^3*p + 6125/8*x^7*v*r^2*j^2*p^2 + 980/3*x^7*v*r^2*j*p^3 + 315/16*x^7*v*r^2*p^4 + 14/15*x^7*v*r*j^5 + 441/8*x^7*v*r*j^4*p + 980/3*x^7*v*r*j^3*p^2 + 980/3*x^7*v*r*j^2*p^3 + 441/8*x^7*v*r*j*p^4 + 14/15*x^7*v*r*p^5 + 1/720*x^7*v*j^6 + 14/15*x^7*v*j^5*p + 315/16*x^7*v*j^4*p^2 + 448/9*x^7*v*j^3*p^3 + 315/16*x^7*v*j^2*p^4 + 14/15*x^7*v*j*p^5 + 1/720*x^7*v*p^6
