A375562 Expansion of e.g.f. 1 / (1 + x * log(1 - x^3)).

1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 1209600, 39916800, 479001600, 1556755200, 79913433600, 1961511552000, 25107347865600, 296406190080000, 11204153985024000, 263564384219136000, 4284610758844416000, 95795516571955200000, 3345240261242880000000

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * |Stirling1(k,n-3*k)|/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^3))))
(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(k, n-3*k, 1))/k!);

Crossrefs

Cf. A052830, A375561.

Cf. A353227.

Sequence in context: A357967 A353227 A375589 * A376347 A376346 A075406

Adjacent sequences: A375559 A375560 A375561 * A375563 A375564 A375565

Keyword

nonn

Author

Seiichi Manyama, Aug 19 2024

Status

approved