Kernel: SageMath 9.2
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[1, 2, 6, 18, 60, 200, 700, 2450, 8820, 31752, 116424]
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A005566: Number of walks of length n on square lattice, starting at origin, staying in first quadrant.
0: a(n) is the number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 5. - _Eric S. Egge_, Oct 21 2008
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(-n^2 - 7*n - 12)*Sn^2 + (8*n + 20)*Sn + 16*n^2 + 48*n + 32
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17523545967408829999363642806657506800280885492603311381994686521023183995818494526343136704823884594622982400835490350268164727785035412382829989246361352225213220805387866514176
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0.00422303415339021
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[4^n*n^(-1)*(1 - 3/2*n^(-1) + O(n^(-2))),
(-4)^n*n^(-3)*(1 - 9/2*n^(-1) + O(n^(-2)))]
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1.25446885783361
1.27133302123899
1.27304859221955
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(16*z^4 - z^2)*Dz^3 + (128*z^3 + 8*z^2 - 6*z)*Dz^2 + (224*z^2 + 28*z - 6)*Dz + 64*z + 12
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(-n^3 - 9*n^2 - 26*n - 24)*Sn^2 + (8*n^2 + 36*n + 40)*Sn + 16*n^3 + 80*n^2 + 128*n + 64
(-n^3 - 9*n^2 - 26*n - 24)*Sn^2 + (8*n^2 + 36*n + 40)*Sn + 16*n^3 + 80*n^2 + 128*n + 64
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(4*z - 1) * (4*z + 1) * z^2
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[z^(-2) - 4*z^(-1)*log(z) - 8*log(z) - 16*z*log(z) - 8*z, z^(-1), 1 + 2*z]
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[log(z - 1/4) - 6*(z - 1/4)*log(z - 1/4) + 31*(z - 1/4)^2*log(z - 1/4), 1 - 14*(z - 1/4)^2, (z - 1/4) - 15/2*(z - 1/4)^2]
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([-1.2732395447351627 +/- 2.54e-17] + [+/- 2.65e-22]*I, [-2.3906971441245563 +/- 1.99e-17] + [4.0000000000000000 +/- 2.78e-17]*I, [12.890661954217663 +/- 2.55e-16] + [-24.000000000000000 +/- 1.12e-16]*I)
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[-1.2732395447351626861510701069801148962756771659236515899813387524711743810738122807209104221300246876485827418140636642951432947689166292230237392858535987138339197354992726205846219711754024615097391431697391812935468991219337890320946590409137815980457275236951206952213916489639152874955027526842297847995715472019893787819156768871865847742645992493358917024375955892175030525982925357139283119669931147888798709447935996995430046813694308674489401501372843723802959040779156829180746701444744199559730824426172542040257625982225311773281835739849567853267248481344242879850712958999906622932354822380405601299254205151107965704870409775950091814510221179031250645443716638278540904994185125596862001960023820788567124552223742810522016801305419681673984928499244916496251718727139876735314816926032604496069722128544177372731260597966617807819702831990012426351265118541792748660383765866297523255998072612616627947763148718624697387405122935160933003656475466210501492002089817437692256900796035 +/- 1.23e-1001] + [+/- 2.93e-1016]*I
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[1.2732395447351627 +/- 2.54e-17] + [+/- 2.65e-22]*I
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1.27323954473516
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