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

0,3

Links

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

Formula

a(n) = 3^n * n! * Sum_{k=0..n} k^(n-k) * binomial(1/3,k)/(n-k)!.

a(n) == 1 (mod 3).

Prog

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

Crossrefs

Cf. A191498, A380134.

Sequence in context: A269906 A092667 A060627 * A113101 A365088 A372013

Adjacent sequences: A380154 A380155 A380156 * A380158 A380159 A380160

Keyword

sign

Author

Seiichi Manyama, Jan 13 2025

Status

approved