A375660 Expansion of e.g.f. 1 / (1 - x * (exp(x) - 1))^2.

1, 0, 4, 6, 80, 370, 4152, 34034, 413632, 4744674, 66354680, 954512482, 15454225536, 263909265074, 4898255210968, 96284064551250, 2022022344889472, 44858682139345090, 1052826609589372152, 25994393541984673154, 674563101823606851520, 18337775305498096349202

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A052848, A375661.

Cf. A005649.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*(exp(x)-1))^2))

PARI

a(n) = n!*sum(k=0, n\2, (k+1)!*stirling(n-k, k, 2)/(n-k)!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052848.

a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)! * Stirling2(n-k,k)/(n-k)!.