A376636 G.f. A(x) satisfies A(x) = (1 + 9*x*A(x)^2)^(1/3).

1, 3, 9, 18, 0, -162, -567, 0, 8019, 31590, 0, -520506, -2160756, 0, 38480265, 164549880, 0, -3072083274, -13390246485, 0, 258054995016, 1139882486490, 0, -22474826957232, -100257845970825, 0, 2011064804461548, 9039247392729582, 0, -183769714890451800

Offset

0,2

Links

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

Formula

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

From Seiichi Manyama, Jun 20 2025: (Start)

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

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

D-finite with recurrence n*(n-2)*a(n) +54*(2*n-5)*(n-4)*a(n-3)=0. - R. J. Mathar, Jul 30 2025

Mathematica

A376636[n_] := 9^n*Binomial[(2*n + 1)/3, n]/(2*n + 1);
Array[A376636, 35, 0] (* Paolo Xausa, Aug 04 2025 *)

Prog

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

Crossrefs

Cf. A004987, A008931, A078532, A245114, A247029, A376282.

Cf. A385117.

Sequence in context: A009216 A103072 A109228 * A355636 A103162 A310331

Adjacent sequences: A376633 A376634 A376635 * A376637 A376638 A376639

Keyword

sign

Author

Seiichi Manyama, Oct 23 2024

Status

approved