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);
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);
A370186
Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^3)^2 )^n.
Original entry on oeis.org
1, 3, 15, 90, 583, 3913, 26790, 185839, 1301575, 9183681, 65181645, 464858661, 3328503814, 23913207750, 172295708971, 1244484142765, 9008351053031, 65332552755149, 474622993450725, 3453219378684621, 25158758123093013, 183521479226172667, 1340195580366321837
Offset: 0
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a(n, s=3, t=2, u=1) = 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.