A360833 Expansion of Sum_{k>=0} ( k * x / (1 - (k * x)^3) )^k.

1, 1, 4, 27, 257, 3189, 48843, 889080, 18731109, 448004763, 11987812504, 354763577414, 11503684020051, 405589341060930, 15447798292502206, 632069580794524857, 27649951709582591394, 1287748889361331630661, 63616184683123273364961

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x/(1-(k*x)^3))^k))
(PARI) a(n) = sum(k=0, n\3, (n-3*k)^n*binomial(n-2*k-1, k));

Crossrefs

Cf. A195242, A360832.

Cf. A338661, A360811, A360835.

Sequence in context: A328694 A353015 A360032 * A360835 A374812 A302836

Adjacent sequences: A360830 A360831 A360832 * A360834 A360835 A360836

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2023

Status

approved