A380017 Expansion of e.g.f. 1/(1 - 3*x*exp(x))^(1/3).

1, 1, 6, 55, 716, 12085, 250726, 6172915, 175903400, 5694587209, 206438732810, 8284550317351, 364605758728828, 17461047965591581, 903964982917764782, 50306323769422679995, 2994799872257498255696, 189906103853462927405329, 12779300537432602189228306

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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. A006153, A380015, A380019.

Sequence in context: A243691 A151345 A281596 * A095652 A132689 A323876

Adjacent sequences: A380014 A380015 A380016 * A380018 A380019 A380020

Keyword

nonn,new

Author

Seiichi Manyama, Jan 09 2025

Status

approved