A375700 Expansion of e.g.f. 1 / (1 + x^3 * log(1 - x))^(1/3).

1, 0, 0, 0, 8, 20, 80, 420, 11648, 100800, 912000, 9055200, 181547520, 2790627840, 41568334080, 635617382400, 13172198645760, 273158953267200, 5632405756723200, 117530452124467200, 2815021136030515200, 71252240659839590400, 1844362570865444044800

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+2)) * |Stirling1(n-3*k,k)|/(6^k*(n-3k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^3*log(1-x))^(1/3)))
(PARI) a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+2)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Crossrefs

Cf. A351504, A375699, A375701.

Sequence in context: A101363 A003685 A066011 * A333156 A365606 A007016

Adjacent sequences: A375697 A375698 A375699 * A375701 A375715 A375716

Keyword

nonn,new

Author

Seiichi Manyama, Aug 25 2024

Status

approved