A360783 Expansion of Sum_{k>=0} x^k / (1 - k*x^3)^(k+1).

1, 1, 1, 1, 3, 7, 13, 24, 55, 133, 301, 678, 1639, 4120, 10253, 25591, 65869, 173551, 459493, 1225379, 3325123, 9162046, 25451181, 71296499, 202144225, 579612934, 1675822453, 4885178596, 14376297345, 42690792651, 127757371105, 385241085261, 1170960103855

Offset

0,5

Links

Table of n, a(n) for n=0..32.

Formula

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^3)^(k+1)))
(PARI) a(n) = sum(k=0, n\3, (n-3*k)^k*binomial(n-2*k, k));

Crossrefs

Cf. A000248, A360782.

Cf. A000930.

Sequence in context: A376707 A309051 A056764 * A026103 A328652 A301854

Adjacent sequences: A360780 A360781 A360782 * A360784 A360785 A360786

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 20 2023

Status

approved