A375652 Expansion of e.g.f. exp(2*x + x^2 * exp(x)).

1, 2, 6, 26, 136, 812, 5494, 41414, 341800, 3056984, 29415274, 302501498, 3305797444, 38212967444, 465409979038, 5951991056558, 79686155008816, 1113909729606896, 16219814971477330, 245503998889083362, 3855373914424695196, 62708526467241370892

Offset: 0

Author

Seiichi Manyama, Aug 22 2024

Keywords

• nonn

Crossrefs

Cf. A216507, A375651.

Cf. A367874, A375629.

Programs

PARI

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

PARI

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

Formula

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