A368963 Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^3 ).
1, 3, 18, 130, 1044, 8949, 80201, 742365, 7042215, 68103156, 668913195, 6654654240, 66916523202, 679039933050, 6944796387690, 71512538784330, 740800257667236, 7714659988543299, 80719544259082000, 848155028673449400, 8945940728543188656
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..952
- Index entries for reversions of series
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^3)/x) -
PARI
a(n, s=2, t=3, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(4*n-k+2,n-2*k).
G.f.: B(x)^3, where B(x) is the g.f. of A365182. - Seiichi Manyama, Sep 20 2024