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