A377268 G.f. satisfies A(x) = (1 - 9*x*A(x))^(1/3).

1, -3, 0, 9, 27, 0, -324, -1215, 0, 18711, 75816, 0, -1301265, -5484996, 0, 100048689, 431943435, 0, -8192222064, -35942240565, 0, 700434986472, 3108770417700, 0, -61805774132388, -276711654879477, 0, 5586291123504300, 25180760594032407, 0, -514555201693265040

Offset: 0

Author

Seiichi Manyama, Oct 22 2024

Keywords

• sign
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for reversions of series

Crossrefs

Cf. A104624.

Programs

Mathematica

A377268[n_] := 9^n*Binomial[(2*n - 4)/3, n]/(n + 1);
Array[A377268, 35, 0] (* Paolo Xausa, Aug 05 2025 *)

PARI

a(n) = 9^n*binomial(2*n/3-4/3, n)/(n+1);

Formula

G.f.: (1/x) * Series_Reversion( x/(1-9*x)^(1/3) ).

a(n) = 9^n * binomial(2*n/3 - 4/3,n)/(n+1).

From Seiichi Manyama, Jun 19 2025: (Start)

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

a(3*n+2) = 0 for n >= 0. (End)