A376282 G.f. A(x) satisfies A(x) = (1 + 9*x*A(x)^7)^(1/3).

1, 3, 54, 1368, 40365, 1299078, 44223732, 1565864784, 57079952046, 2127818007315, 80742077597610, 3108398557803480, 121107814518484872, 4766365291226837508, 189209375036491438800, 7567095678024459993120, 304603864960375133224533, 12331716699093681951702810

Offset: 0

Author

Seiichi Manyama, Oct 23 2024

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..600

Crossrefs

Cf. A004987, A008931, A078532, A245114, A376636.

Programs

Mathematica

A376282[n_] := 9^n*Binomial[(7*n + 1)/3, n]/(7*n + 1);
Array[A376282, 20, 0] (* Paolo Xausa, Aug 04 2025 *)

PARI

a(n) = 9^n*binomial(7*n/3+1/3, n)/(7*n+1);

Formula

a(n) = 9^n * binomial(7*n/3 + 1/3,n)/(7*n+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^11). - Seiichi Manyama, Jun 20 2025

D-finite with recurrence 8*n*(n-1)*(n-2)*(4*n-5)*(2*n-1)*(4*n+1)*a(n) -189*(7*n-11)*(7*n-17)*(7*n-2)*(7*n-20)*(7*n-5)*(7*n-8)*a(n-3)=0. - R. J. Mathar, Jul 30 2025