A380159 Expansion of e.g.f. (exp(-3*x) + 3*x)^(1/3).
1, 0, 3, -9, -27, 459, 243, -58563, 338985, 11581623, -206336889, -2610099207, 128764066797, 37135699587, -90848500643781, 1216300295221749, 68623945856512209, -2410073970973057809, -44786917868989757553, 4171855691698864732305, -8174731579262161250859
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, 3^k*(3*k-1)^(n-k)*binomial(1/3, k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} 3^k * (3*k-1)^(n-k) * binomial(1/3,k)/(n-k)!.
a(n) == 0 (mod 3) for n>0.