A380156 Expansion of e.g.f. 1/(1 - 3*x*exp(3*x))^(1/3).
1, 1, 10, 127, 2260, 52165, 1478098, 49666267, 1930817080, 85253566825, 4214519350750, 230609701370719, 13837049296702228, 903380930924784013, 63754235596937808874, 4836352735401636409795, 392451456493513697671792, 33920902255644870783973201, 3111255003645991777552833718
Offset: 0
Keywords
Programs
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PARI
a(n) = 3^n*n!*sum(k=0, n, (-1)^k*k^(n-k)*binomial(-1/3, k)/(n-k)!);
Formula
a(n) = 3^n * n! * Sum_{k=0..n} (-1)^k * k^(n-k) * binomial(-1/3,k)/(n-k)!.
a(n) == 1 (mod 9).