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

0,3

Links

Table of n, a(n) for n=0..20.

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.

Prog

(PARI) a(n) = n!*sum(k=0, n, 3^k*(3*k-1)^(n-k)*binomial(1/3, k)/(n-k)!);

Crossrefs

Cf. A380016, A380158.

Sequence in context: A032261 A300981 A018924 * A061582 A175129 A336793

Adjacent sequences: A380156 A380157 A380158 * A380160 A380161 A380162

Keyword

sign

Author

Seiichi Manyama, Jan 13 2025

Status

approved