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

0,3

Links

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

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!.

Prog

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

Crossrefs

Cf. A321837, A362164, A362188.

Sequence in context: A006531 A326550 A352236 * A242369 A202617 A143633

Adjacent sequences: A362202 A362203 A362204 * A362206 A362207 A362208

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 11 2023

Status

approved