A362309 Expansion of e.g.f. exp(x - x^3/3).

1, 1, 1, -1, -7, -19, 1, 211, 1009, 953, -14239, -105049, -209879, 1669669, 18057313, 56255291, -294375199, -4628130319, -19929569471, 70149241423, 1652969810521, 9226206209501, -20236475188159, -783908527648861, -5452368869656367

Offset: 0

Author

Seiichi Manyama, Apr 15 2023

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..632

Crossrefs

Column k=2 of A362302.

Cf. A001470, A246607.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-x^3/3)))

Formula

a(n) = a(n-1) - 2 * binomial(n-1,2) * a(n-3) for n > 2.

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