A375629 Expansion of e.g.f. exp(2*x) / (1 - x^2 * exp(x)).

1, 2, 6, 26, 148, 1052, 8974, 89294, 1015480, 12991832, 184682554, 2887850858, 49261993444, 910356170804, 18117379906630, 386315966673638, 8786555389140976, 212335975835710256, 5433155029435593970, 146744457899073450050, 4172032796528725318876

Offset: 0

Author

Seiichi Manyama, Aug 21 2024

Keywords

• nonn

Crossrefs

Cf. A368265, A375630.

Cf. A358080.

Programs

PARI

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

PARI

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

Formula

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