A373517 Expansion of e.g.f. exp(x/(1 - x^3)^(1/3)).

1, 1, 1, 1, 9, 41, 121, 1401, 11761, 61489, 864081, 10597841, 81833401, 1350154521, 21715461769, 225232218121, 4267472824161, 84597818284001, 1111699778741281, 23801969674626849, 558853937533757161, 8943028907965939081, 213696639293901810201

Offset

0,5

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) == 1 mod 8.

Prog

(PARI) a(n) = n!*sum(k=0, n\3, binomial(n/3-1, k)/(n-3*k)!);

Crossrefs

Cf. A293493, A373518.

Cf. A373522.

Sequence in context: A018836 A373522 A245932 * A362293 A274323 A297740

Adjacent sequences: A373514 A373515 A373516 * A373518 A373519 A373520

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2024

Status

approved