A369594 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * (1+x^3)^3) ).

1, 3, 12, 58, 318, 1887, 11772, 75969, 502554, 3389056, 23211312, 161015058, 1128976523, 7988381001, 56968671948, 409046328954, 2954644519365, 21455293440345, 156534285598068, 1146881543952792, 8434926025730955, 62250461094154372, 460859182211975184

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

Prog

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

Crossrefs

Cf. A369441.

Sequence in context: A163047 A369616 A372378 * A369403 A291488 A090363

Adjacent sequences: A369591 A369592 A369593 * A369595 A369596 A369597

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2024

Status

approved