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

0,5

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A028310, A380133.

Cf. A380051, A380094.

Cf. A380017.

Sequence in context: A199494 A171791 A060908 * A322442 A036449 A051500

Adjacent sequences: A380131 A380132 A380133 * A380135 A380136 A380137

Keyword

sign,new

Author

Seiichi Manyama, Jan 12 2025

Status

approved