A360815 Expansion of Sum_{k>=0} x^(3*k) / (1 - k*x)^(k+1).

1, 0, 0, 1, 2, 3, 5, 11, 30, 88, 260, 771, 2343, 7474, 25380, 91650, 347988, 1371873, 5570173, 23233703, 99676434, 440931977, 2014619700, 9506385864, 46246356169, 231348803925, 1187212953132, 6239006165820, 33546182775824, 184497923546700

Offset: 0

Author

Seiichi Manyama, Feb 21 2023

Keywords

• nonn

Crossrefs

Cf. A360709.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/(1-k*x)^(k+1)))

PARI

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

Formula

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