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

0,3

Links

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

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!.

Prog

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

Crossrefs

Cf. A321837, A362164, A362205.

Sequence in context: A231277 A188365 A107720 * A299425 A360618 A060053

Adjacent sequences: A362185 A362186 A362187 * A362189 A362190 A362191

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 11 2023

Status

approved