A377532 Expansion of e.g.f. 1/(1 - x^2 * exp(x))^3.
1, 0, 6, 18, 180, 1500, 15930, 191646, 2580648, 38683224, 636068430, 11392350090, 220658360076, 4594593295188, 102333126352002, 2427278515815510, 61079333377870800, 1625065147997303856, 45576552142354413078, 1343802083242003570818, 41552482139458105525620
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(k+2, 2)/(n-2*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k) * binomial(k+2,2)/(n-2*k)!.
a(n) ~ n! * n^2 / ((1 + LambertW(1/2))^3 * 2^(n+4) * LambertW(1/2)^n). - Vaclav Kotesovec, Oct 31 2024