A373539 Expansion of e.g.f. exp(x/(1 + x^3)^(1/3)).

1, 1, 1, 1, -7, -39, -119, 841, 10641, 59473, -393679, -9119439, -77841719, 453247081, 17769103353, 210702481081, -1002688100959, -65813075987679, -1022777654395679, 3554736409105633, 413233827275657241, 8091508938651283321, -16214426267734966039

Offset

0,5

Links

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

Formula

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

a(n) == 1 mod 8.

Prog

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

Crossrefs

Cf. A012019, A373540.

Cf. A373517.

Sequence in context: A304012 A329528 A215441 * A027482 A352310 A196782

Adjacent sequences: A373536 A373537 A373538 * A373540 A373541 A373542

Keyword

sign

Author

Seiichi Manyama, Jun 09 2024

Status

approved