A380017 Expansion of e.g.f. 1/(1 - 3*x*exp(x))^(1/3).
1, 1, 6, 55, 716, 12085, 250726, 6172915, 175903400, 5694587209, 206438732810, 8284550317351, 364605758728828, 17461047965591581, 903964982917764782, 50306323769422679995, 2994799872257498255696, 189906103853462927405329, 12779300537432602189228306
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (-3)^k*k^(n-k)*binomial(-1/3, k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} (-3)^k * k^(n-k) * binomial(-1/3,k)/(n-k)!.
a(n) ~ sqrt(2*Pi) * n^(n - 1/6) / (Gamma(1/3) * (1 + LambertW(1/3))^(1/3) * exp(n) * LambertW(1/3)^n). - Vaclav Kotesovec, Jan 23 2025