A369484
Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^3)^2) ).
Original entry on oeis.org
1, 3, 12, 57, 301, 1700, 10045, 61303, 383335, 2443113, 15811317, 103627692, 686402602, 4587643765, 30900426417, 209539509967, 1429344492215, 9801262309209, 67523359213569, 467136798336153, 3243948604314619, 22604271635042853, 158001453530915361
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^3)^2))/x)
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a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
A369485
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^3)^2) ).
Original entry on oeis.org
1, 4, 22, 142, 1007, 7590, 59683, 484112, 4021061, 34029532, 292373296, 2543542676, 22360917140, 198341377680, 1772860026933, 15952960500612, 144397901220980, 1313835276189792, 12009823111155481, 110240431974732436, 1015727265740887873
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x+x^3)^2))/x)
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a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
A370185
Coefficient of x^n in the expansion of (1+x+x^3)^(2*n).
Original entry on oeis.org
1, 2, 6, 26, 126, 612, 2970, 14534, 71838, 357884, 1793296, 9026976, 45612450, 231224060, 1175422590, 5989693176, 30586693182, 156483812892, 801908994852, 4115509738188, 21149522157816, 108817959549416, 560500440662872, 2889915938877078, 14913928051929426
Offset: 0
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a(n, s=3, t=2, u=0) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
A372375
Expansion of (1/x) * Series_Reversion( x * (1+x) / (1+x+x^3)^2 ).
Original entry on oeis.org
1, 1, 1, 3, 9, 21, 54, 161, 470, 1347, 4007, 12199, 37141, 113802, 352905, 1101969, 3455220, 10891968, 34515825, 109814395, 350616323, 1123368287, 3610647348, 11637410625, 37605280548, 121812321775, 395455199269, 1286446544052, 4192913001804, 13690359696969
Offset: 0
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my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1+x)/(1+x+x^3)^2)/x)
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a(n, s=3, t=2, u=-1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
A369507
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^3)^2 ).
Original entry on oeis.org
1, 6, 51, 508, 5535, 63888, 767689, 9502254, 120324606, 1551362160, 20296839585, 268785905790, 3595951246855, 48528885742200, 659856371680971, 9031161933443468, 124319953470044970, 1720113658097639532, 23908612149570793386, 333680424238179500976
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^3)^2)/x)
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a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-3*k))/(n+1);
Showing 1-5 of 5 results.