A360810 Expansion of Sum_{k>=0} ( x / (1 - k * x^2) )^k.

1, 1, 1, 2, 5, 11, 29, 81, 229, 696, 2181, 7045, 23653, 81433, 288173, 1046814, 3887749, 14768783, 57275541, 226462801, 912443397, 3741515804, 15603500797, 66134448329, 284660214181, 1243605590897, 5511058189989, 24760003963802, 112726590916645

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k*x^2))^k))
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^k*binomial(n-k-1, k));

Crossrefs

Cf. A324158, A360782.

Sequence in context: A316769 A192785 A334578 * A320171 A014211 A160911

Adjacent sequences: A360807 A360808 A360809 * A360811 A360812 A360813

Keyword

nonn

Author

Seiichi Manyama, Feb 21 2023

Status

approved