A369443 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3)) ).

1, 2, 5, 15, 52, 198, 796, 3306, 14042, 60698, 266235, 1182315, 5306085, 24028162, 109654887, 503797703, 2328343326, 10816971516, 50487762906, 236635814984, 1113297830297, 5255647026534, 24888156618738, 118194065746758, 562773777767295, 2686074452484012

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,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)))/x)
(PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial(u*(n+1), n-s*k))/(n+1);

Crossrefs

Cf. A198951.

Sequence in context: A287276 A361762 A367415 * A369398 A370798 A007312

Adjacent sequences: A369440 A369441 A369442 * A369444 A369445 A369446

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2024

Status

approved