A369483
Expansion of (1/x) * Series_Reversion( x / (1+x+x^3)^2 ).
Original entry on oeis.org
1, 2, 5, 16, 60, 242, 1014, 4370, 19278, 86678, 395751, 1829742, 8549100, 40302810, 191469165, 915751966, 4405727502, 21307102900, 103526683797, 505118705078, 2473833623696, 12157124607612, 59929746189165, 296271556144028, 1468494529164194, 7296261411708962
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^3)^2)/x)
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a(n, s=3, t=2, u=0) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
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);
A370187
Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^3)^2 )^n.
Original entry on oeis.org
1, 4, 28, 226, 1940, 17214, 155914, 1432106, 13289076, 124276528, 1169346298, 11057293526, 104986087178, 1000248093420, 9557756114130, 91559051752596, 879027678226452, 8455595252761536, 81476137225450096, 786286875175380088, 7598503022428758570
Offset: 0
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a(n, s=3, t=2, u=2) = 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);
Showing 1-4 of 4 results.