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

Author

Seiichi Manyama, Jan 13 2025

Keywords

• nonn

Crossrefs

Cf. A006153, A380155.

Cf. A380016, A380017.

Programs

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).