A375795 Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x).

1, 1, 2, 9, 48, 320, 2580, 24150, 258720, 3117744, 41741280, 614774160, 9877412160, 171923225760, 3222634615200, 64721762305200, 1386495651340800, 31558444491974400, 760564843136017920, 19348085890139086080, 518103061345155686400, 14567452481227893811200

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A000670, A375796.

Cf. A357962.

Programs

PARI

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

PARI

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

Formula

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