A375627 Expansion of e.g.f. exp(2*x^2) / (1 - x * exp(x^2)).

1, 1, 6, 24, 168, 1260, 11760, 126000, 1545600, 21304080, 326350080, 5497873920, 101048048640, 2011924474560, 43139969832960, 991088998099200, 24286975237324800, 632358338278867200, 17433184834127462400, 507307459608530380800, 15539683835941532467200

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^2)/(1-x*exp(x^2))))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+2)^k/k!);

Crossrefs

Cf. A368265, A375628.

Cf. A358064, A375604.

Sequence in context: A221980 A359693 A225827 * A349498 A200904 A293488

Adjacent sequences: A375624 A375625 A375626 * A375628 A375629 A375630

Keyword

nonn

Author

Seiichi Manyama, Aug 21 2024

Status

approved