A368318 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3)^2) ).

1, 2, 5, 16, 62, 264, 1170, 5310, 24599, 116090, 556569, 2703098, 13268900, 65721840, 328050639, 1648535856, 8333536002, 42348587700, 216211838178, 1108514508608, 5704874555112, 29460504457692, 152612723209700, 792833380805160, 4129639139612133

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Index entries for reversions of series

Formula

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

Prog

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

Crossrefs

Cf. A369442, A369443.

Sequence in context: A007976 A058259 A361920 * A369400 A033543 A124531

Adjacent sequences: A368315 A368316 A368317 * A368319 A368320 A368321

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2024

Status

approved