A373522 Expansion of e.g.f. exp(x * (1 + x^3)^(1/3)).

1, 1, 1, 1, 9, 41, 121, -279, -1679, 1009, 259281, 1173041, 669241, -267141159, -1295686391, 10821721, 650092657761, 3480768830561, 17723446561, -2911516748764191, -17068971040559639, 427036022281, 21673592659354854681, 137752098937383025481

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

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

a(n) == 1 mod 8.

Prog

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

Crossrefs

Cf. A190875, A373523.

Cf. A373517.

Sequence in context: A273359 A251422 A018836 * A245932 A373517 A362293

Adjacent sequences: A373519 A373520 A373521 * A373523 A373524 A373525

Keyword

sign

Author

Seiichi Manyama, Jun 08 2024

Status

approved