A377533 Expansion of e.g.f. 1/(1 - x * exp(x^2))^2.

1, 2, 6, 36, 264, 2280, 23760, 283920, 3830400, 57728160, 959212800, 17424348480, 343508014080, 7302340805760, 166504724305920, 4053311579116800, 104916366780825600, 2877212787562713600, 83332056329006284800, 2541707625791324390400, 81432631127484628992000

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1) * (n-2*k)^k/k!.

a(n) ~ n! * n * 2^(n/2) / ((1+LambertW(2))^2 * LambertW(2)^(n/2)). - Vaclav Kotesovec, Oct 31 2024

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)*(n-2*k)^k/k!);

Crossrefs

Cf. A358064, A377534.

Sequence in context: A358080 A369091 A162697 * A107099 A143021 A007657

Adjacent sequences: A377530 A377531 A377532 * A377534 A377535 A377536

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 31 2024

Status

approved