A377531 Expansion of e.g.f. 1/(1 - x^2 * exp(x))^2.

1, 0, 4, 12, 96, 760, 7260, 80724, 1008112, 14079888, 216881460, 3652767580, 66773963784, 1316433381432, 27840054610732, 628626642921060, 15093709672205280, 383989133237230624, 10317497504580922212, 291958800400148127660, 8678485827979443326200

Offset

0,3

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A358080, A377532.

Sequence in context: A287596 A364901 A268363 * A038053 A217155 A120267

Adjacent sequences: A377528 A377529 A377530 * A377532 A377533 A377534

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 31 2024

Status

approved