A368265 Expansion of e.g.f. exp(2*x) / (1 - x*exp(x)).

1, 3, 12, 65, 460, 4057, 42922, 529769, 7472808, 118586033, 2090936014, 40554647377, 858082563532, 19668880007129, 485528656965762, 12841428220413593, 362276791422785488, 10859170086870710497, 344648459867067117334, 11546148650974694099201

Offset: 0

Author

Seiichi Manyama, Dec 19 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A006153, A072597, A092148, A368266.

Cf. A368267, A368271.

Programs

PARI

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

Formula

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

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