A385117 G.f. A(x) satisfies A(x) = 1 + 9*x*A(x)^(2/3).

1, 9, 54, 243, 810, 1701, 0, -16038, -56862, 0, 817938, 3241134, 0, -53872371, -224386200, 0, 4017339666, 17216031195, 0, -322568743770, -1408090130370, 0, 27206369474544, 120309415164990, 0, -2376712950727284, -10611290417552118, 0, 213172869272924088

Offset: 0

Author

Seiichi Manyama, Jun 18 2025

Keywords

• sign
• changed

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A135864, A214668, A385119.

Cf. A376636.

Programs

Mathematica

A385117[n_] := 9^n*Binomial[2*n/3 + 1, n]/(2*n/3 + 1);
Array[A385117, 35, 0] (* Paolo Xausa, Aug 01 2025 *)

PARI

a(n) = 9^n*binomial(2*n/3+1, n)/(2*n/3+1);

Formula

a(n) = 9^n * binomial(2*n/3+1,n)/(2*n/3+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^(1/3)).

G.f.: 1/B(-x), where B(x) is the g.f. of A135864.

G.f.: B(x)^3, where B(x) is the g.f. of A376636.

a(3*n) = 0 for n > 1.

D-finite with recurrence (n-1)*(n-2)*a(n) + 54*(2*n-3)*(n-6)*a(n-3) = 0. - R. J. Mathar, Jul 30 2025

a(n) ~ A128834(n) * 2^(2*n/3) * 3^(n+3/2) / (sqrt(Pi) * n^(3/2)). - Amiram Eldar, Sep 02 2025