A380134 Expansion of e.g.f. (1 + 3*x*exp(x))^(1/3).

1, 1, 0, 1, -4, 25, -194, 1813, -19816, 248113, -3502630, 55052701, -953576876, 18048491305, -370623627178, 8207063150245, -194950421191504, 4944881412682081, -133394451535683278, 3813510163227155245, -115170227064335439700, 3663942710200202043481

Offset: 0

Author

Seiichi Manyama, Jan 12 2025

Keywords

• sign

Crossrefs

Cf. A028310, A380133.

Cf. A380051, A380094.

Cf. A380017.

Programs

PARI

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

Formula

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