A377534 Expansion of e.g.f. 1/(1 - x * exp(x^2))^3.
1, 3, 12, 78, 648, 6300, 72000, 939960, 13749120, 223035120, 3969907200, 76890733920, 1609732776960, 36214043785920, 871131980759040, 22310233170825600, 606026217929932800, 17401756135956192000, 526641334386809241600, 16753142420507766873600
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n-2*k+2, 2)/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n-2*k+2,2)/k!.
a(n) ~ n! * n^2 * 2^(n/2 - 1) / ((1 + LambertW(2))^3 * LambertW(2)^(n/2)). - Vaclav Kotesovec, Oct 31 2024