A375661 Expansion of e.g.f. 1 / (1 - x * (exp(x) - 1))^3.

1, 0, 6, 9, 156, 735, 9738, 83181, 1129656, 13662459, 207281190, 3151269033, 54457383060, 980680471095, 19240001086530, 397345461622245, 8763618490102128, 203472380293912563, 4991552271140255838, 128517790560854181537, 3472936316648987980620

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A052848, A375660.

Cf. A226515.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*(exp(x)-1))^3))

PARI

a(n) = n!*sum(k=0, n\2, (k+2)!*stirling(n-k, k, 2)/(n-k)!)/2;

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052848.

a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (k+2)! * Stirling2(n-k,k)/(n-k)!.