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

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

Cf. A369483, A369484, A369485.

Cf. A372371.

Sequence in context: A272265 A191796 A367111 * A345108 A007056 A026551

Adjacent sequences: A372372 A372373 A372374 * A372376 A372377 A372378

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved