A360811 Expansion of Sum_{k>=0} ( x / (1 - k * x^3) )^k.

1, 1, 1, 1, 2, 5, 10, 18, 38, 91, 211, 472, 1108, 2754, 6881, 17101, 43443, 113565, 300142, 797191, 2147414, 5883976, 16293712, 45471429, 128285353, 366266188, 1055534118, 3066483484, 8989837397, 26602652605, 79370560477, 238606427241, 722973445270

Offset: 0

Author

Seiichi Manyama, Feb 21 2023

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A324158, A360783.

Programs

Maple

N:= 100:
F:= 1 + add((x/(1-k*x^3))^k, k=1..N):
S:= series(F,x,N+1):
seq(coeff(S,x,k),k=0..N); # Robert Israel, Feb 21 2024

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k*x^3))^k))

PARI

a(n) = sum(k=0, n\3, (n-3*k)^k*binomial(n-2*k-1, k));

Formula

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