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