A377684 Expansion of e.g.f. (1 - x * log(1 - x))^4.

1, 0, 8, 12, 176, 840, 7416, 58800, 529728, 5152896, 54070560, 612342720, 7472424384, 97979207040, 1375839795456, 20619488373120, 328716465177600, 5556948993792000, 99324048442208256, 1871986425192990720, 37110785352536724480, 772059856808638218240, 16820447458491885035520

Offset

0,3

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} k! * binomial(4,k) * |Stirling1(n-k,k)|/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\2, k!*binomial(4, k)*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A377682, A377683.

Sequence in context: A258780 A228663 A377681 * A076028 A281256 A070476

Adjacent sequences: A377681 A377682 A377683 * A377685 A377686 A377687

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 04 2024

Status

approved