A369482 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^3)) ).

1, 3, 12, 56, 287, 1564, 8895, 52195, 313655, 1920489, 11938271, 75143016, 477948051, 3067190311, 19835032603, 129129612163, 845603794947, 5566269982581, 36810651063798, 244448822313138, 1629413356387998, 10898124891668031, 73116947514706451

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+1,k) * binomial(3*n-k+3,n-3*k).

Prog

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

Crossrefs

Cf. A071879, A369481.

Sequence in context: A276902 A192132 A179486 * A366097 A074533 A000257

Adjacent sequences: A369479 A369480 A369481 * A369483 A369484 A369485

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2024

Status

approved