A369505 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x)^2 ).

1, 8, 86, 1066, 14361, 204314, 3020745, 45955442, 714723588, 11312450432, 181625888244, 2950848879096, 48423670556100, 801454908292020, 13363137183238881, 224253208102065664, 3784736105491395780, 64197997357038408976, 1093863031541592651003

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x)^2)/x)
(PARI) a(n) = sum(k=0, n, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-k))/(n+1);

Crossrefs

Cf. A003645, A369502.

Sequence in context: A230621 A357420 A371407 * A378692 A268052 A268075

Adjacent sequences: A369502 A369503 A369504 * A369506 A369507 A369508

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2024

Status

approved