A358080 Expansion of e.g.f. 1/(1 - x^2 * exp(x)).

1, 0, 2, 6, 36, 260, 2190, 21882, 248696, 3181320, 45229050, 707208590, 12063902532, 222939837276, 4436813677478, 94605994108290, 2151763873634160, 51999544476324752, 1330540380342907506, 35936656483848501654, 1021700660649312689660

Offset: 0

Author

Seiichi Manyama, Oct 30 2022

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..425

Crossrefs

Cf. A006153, A358081.

Cf. A216507, A345747, A358064.

Programs

PARI

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

PARI

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

Formula

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

a(n) ~ n! / ((1 + LambertW(1/2)) * 2^(n+1) * LambertW(1/2)^n). - Vaclav Kotesovec, Oct 30 2022