A366459 Expansion of e.g.f. -log(1 - x^2 * exp(x)).

0, 0, 2, 6, 24, 140, 990, 8442, 84056, 955656, 12227130, 173812430, 2717859012, 46362339036, 856770362630, 17050946225250, 363576478312560, 8269357341437072, 199837364514425586, 5113346326011170838, 138106722548779770620, 3926456810081828991780

Offset: 0

Author

Seiichi Manyama, Dec 14 2023

Keywords

• nonn

Crossrefs

Cf. A009444, A366546.

Cf. A216507, A346753, A358080.

Programs

PARI

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

Formula

a(n) = n! * Sum_{k=1..floor(n/2)} k^(n-2*k-1)/(n-2*k)!.

a(n) ~ (n-1)! / (2^n *LambertW(1/2)^n). - Vaclav Kotesovec, Dec 29 2023