A380051 E.g.f. A(x) satisfies A(x) = ( 1 + 3*x*exp(x)*A(x) )^(1/3).

1, 1, 2, 1, -12, -15, 526, 1617, -49608, -302111, 8126010, 85724001, -2020009628, -34232466255, 696686324166, 18267485751985, -310973114236944, -12533263924965183, 168118610439268594, 10727427541319225793, -100693940482485604260, -11178369799980253348079

Offset: 0

Author

Seiichi Manyama, Jan 11 2025

Keywords

• sign

Crossrefs

Cf. A006153, A380050.

Cf. A380047.

Programs

PARI

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

Formula

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