A369214 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-x^3) ).

1, 2, 7, 31, 155, 833, 4696, 27393, 163944, 1001022, 6211049, 39048685, 248213672, 1592561156, 10300192220, 67083304750, 439571860881, 2895898913453, 19169805142929, 127442939722175, 850536450459795, 5696270624620125, 38271171118343550

Offset

0,2

Links

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

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2-x^3))/x)
(PARI) a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(3*n-k+1, n-3*k))/(n+1);

Crossrefs

Cf. A151374, A249924, A369160.

Cf. A049140, A369114.

Sequence in context: A366052 A368931 A007863 * A302061 A030823 A030873

Adjacent sequences: A369211 A369212 A369213 * A369215 A369216 A369217

Keyword

nonn

Author

Seiichi Manyama, Jan 16 2024

Status

approved