A372375 - OEIS

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A372375

Expansion of (1/x) * Series_Reversion( x * (1+x) / (1+x+x^3)^2 ).

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

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..29.

Index entries for reversions of series

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(n-k+1,n-3*k).

PROG

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1+x)/(1+x+x^3)^2)/x)

(PARI) 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);

CROSSREFS