A380157 Expansion of e.g.f. (1 + 3*x*exp(3*x))^(1/3).
1, 1, 4, 1, -44, 265, 2458, -48419, -99320, 12598417, -82133810, -4205894891, 86494587292, 1457086105657, -79743685096670, -88062957588275, 77425160027442832, -1138977883460384735, -76951663963327663082, 2978943480750081242629, 64353221406902873516260
Offset: 0
Keywords
Programs
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PARI
a(n) = 3^n*n!*sum(k=0, n, k^(n-k)*binomial(1/3, k)/(n-k)!);
Formula
a(n) = 3^n * n! * Sum_{k=0..n} k^(n-k) * binomial(1/3,k)/(n-k)!.
a(n) == 1 (mod 3).