A379995 Expansion of e.g.f. exp(-2*x)/(exp(-x) - x)^4.
1, 6, 48, 476, 5608, 76372, 1179016, 20332580, 387225120, 8068825988, 182564048824, 4456476380644, 116724944900272, 3264981100202564, 97130013288324552, 3062011655207131748, 101963095705628194624, 3576126056313566090500, 131762871920106615643480
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n, (k+2)^(n-k)*binomial(k+3, 3)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} (k+2)^(n-k) * binomial(k+3,3)/(n-k)!.
a(n) ~ n! * n^3 / (6 * (LambertW(1) + 1)^4 * LambertW(1)^(n+2)). - Vaclav Kotesovec, Jan 08 2025