A369269 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^3)^3 ).

1, 2, 7, 33, 173, 962, 5586, 33498, 205846, 1289386, 8202247, 52845855, 344129832, 2261377872, 14976646685, 99863119809, 669860309538, 4517037850220, 30603008068997, 208211448723097, 1421986458302466, 9745007758311114, 66993247112160800

Offset

0,2

Links

Table of n, a(n) for n=0..22.

P. Bala, Fractional iteration of a series inversion operator

Index entries for reversions of series

Formula

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

a(n) = (1/(n+1)) * [x^n] ( 1/(1-x)^2 * (1+x^3)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A369268, A369270.

Cf. A369265, A369267.

Sequence in context: A162257 A214954 A366237 * A369300 A055724 A301433

Adjacent sequences: A369266 A369267 A369268 * A369270 A369271 A369272

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2024

Status

approved