A375716 Expansion of e.g.f. 1 / (1 - x^3 * (exp(x) - 1))^(1/6).

1, 0, 0, 0, 4, 10, 20, 35, 3976, 35364, 205920, 970365, 37643980, 670990606, 7705037704, 69043474955, 1690055888080, 43135620048200, 793592298255936, 11401734214307769, 250361353418216340, 7380072768323315410, 187670442928777057480, 3868359812089009616071

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+1)) * Stirling2(n-3*k,k)/(6^k*(n-3k)!).

Prog

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

Crossrefs

Cf. A358014, A375717, A375718.

Sequence in context: A355308 A356952 A356963 * A370992 A355180 A341656

Adjacent sequences: A375700 A375701 A375715 * A375717 A375718 A375721

Keyword

nonn,new

Author

Seiichi Manyama, Aug 25 2024

Status

approved