A375717 Expansion of e.g.f. 1 / (1 - x^3 * (exp(x) - 1))^(1/3).

1, 0, 0, 0, 8, 20, 40, 70, 9072, 80808, 470640, 2217930, 91956920, 1649007932, 18956858648, 169921752910, 4310715370080, 111302746115920, 2053356893604192, 29525879498171538, 660295352236840680, 19735183465373056100, 504257138580203577800

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)) * 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))^(1/3)))
(PARI) a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+2)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));

Crossrefs

Cf. A358014, A375716, A375718.

Sequence in context: A351967 A086062 A006416 * A273069 A273144 A272842

Adjacent sequences: A375701 A375715 A375716 * A375718 A375721 A375722

Keyword

nonn,new

Author

Seiichi Manyama, Aug 25 2024

Status

approved