A362188 Expansion of e.g.f. exp(x/(1-3*x)^(2/3)).

1, 1, 5, 43, 513, 7781, 142861, 3075255, 75879553, 2110145833, 65275127541, 2222656864451, 82595058938305, 3325666654250253, 144214230714973693, 6700048267934377231, 331988586859256529921, 17475202293073669341905, 973765103770578798536293

Offset: 0

Author

Seiichi Manyama, Apr 11 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A321837, A362164, A362205.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-3*x)^(2/3))))

Formula

a(n) = n! * Sum_{k=0..n} (-3)^k * binomial(-2*(n-k)/3,k)/(n-k)! = n! * Sum_{k=0..n} 3^(n-k) * binomial(n-k/3-1,n-k)/k!.