A375631 Expansion of e.g.f. exp(2*x) / (1 - x^2/2 * exp(x)).

1, 2, 5, 17, 76, 422, 2809, 21821, 193708, 1934468, 21465529, 262007033, 3488768650, 50326173458, 781808322481, 13012772925293, 231029881905736, 4358082011900744, 87045479653871377, 1835177785479753545, 40727378713879346206, 949039029924830652662

Offset: 0

Author

Seiichi Manyama, Aug 21 2024

Keywords

• nonn

Crossrefs

Cf. A368265, A375632.

Programs

PARI

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

PARI

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

Formula

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