A362205 Expansion of e.g.f. exp(x/(1-3*x)^(1/3)).

1, 1, 3, 19, 185, 2401, 38731, 745123, 16630769, 422157025, 12005107091, 377957000851, 13048046175913, 490052749100929, 19890724260375515, 867582126490694371, 40467070835396193761, 2009901604798183428673, 105901641663222888913699

Offset: 0

Author

Seiichi Manyama, Apr 11 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A321837, A362164, A362188.

Programs

PARI

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

Formula

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