A369398 Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3) ).

1, 2, 5, 15, 52, 198, 797, 3322, 14195, 61848, 273792, 1228131, 5570200, 25501610, 117694557, 546983631, 2557677780, 12024345942, 56801925455, 269483935384, 1283469626512, 6134259516564, 29412031039568, 141434223863670, 681939435678239, 3296147009539144

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+k,k) * binomial(2*n+2,n-3*k).

a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 / (1-x^3) )^(n+1). - Seiichi Manyama, Feb 16 2024

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-1, k)*binomial(u*(n+1), n-s*k))/(n+1);

Crossrefs

Cf. A215340, A369297.

Cf. A370213.

Sequence in context: A361762 A367415 A369443 * A370798 A007312 A007296

Adjacent sequences: A369395 A369396 A369397 * A369399 A369400 A369401

Keyword

nonn

Author

Seiichi Manyama, Jan 22 2024

Status

approved