A385119 G.f. A(x) satisfies A(x) = 1 + 9*x*A(x)^(5/3).

1, 9, 135, 2430, 48195, 1015740, 22320522, 505692720, 11727186075, 277005649635, 6641224015140, 161193712078854, 3953072078945730, 97801207953712200, 2438092322304120720, 61182608813245896840, 1544295394480280288715, 39180450803555268621540

Offset: 0

Author

Seiichi Manyama, Jun 18 2025

Keywords

• nonn
• changed

Links

• Paolo Xausa, Table of n, a(n) for n = 0..650

Crossrefs

Cf. A135864, A214668, A385117.

Cf. A245114.

Programs

Mathematica

A385119[n_] := 9^n*Binomial[#, n]/# & [5*n/3 + 1];
Array[A385119, 20, 0] (* Paolo Xausa, Aug 05 2025 *)

PARI

a(n) = 9^n*binomial(5*n/3+1, n)/(5*n/3+1);

Formula

a(n) = 9^n * binomial(5*n/3+1,n)/(5*n/3+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^(7/3)).

G.f.: B(x)^3, where B(x) is the g.f. of A245114.

D-finite with recurrence 2*n*(n-1)*(n-2)*(2*n+3)*a(n) - 135*(5*n-9)*(5*n-3)*(5*n-12)*(5*n-6)*a(n-3) = 0. - R. J. Mathar, Jul 30 2025

a(n) ~ 3^(n+1) * 5^(5*n/3+1/2) / (sqrt(Pi) * 2^(2*(n+3)/3) * n^(3/2)). - Amiram Eldar, Sep 02 2025