A025762 9th-order Vatalan numbers (generalization of Catalan numbers).

1, 1, 37, 1909, 112483, 7123123, 472012183, 32269160215, 2256940619488, 160620490138312, 11588554266307408, 845405636848547320, 62239772654736987376, 4617428134374127211320, 344799253687326693132448

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000108, A025756, A025757, A025758, A025759, A025760, A025761, A025763.

Programs

Mathematica

Table[SeriesCoefficient[9/(8 + (1 - 81 x)^(1/9)), {x, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Dec 29 2012 *)

Formula

G.f.: 9/(8 + (1 - 81*x)^(1/9)).

a(n) = (-1)^(n+1) * 9^(2*n+1) * Sum_{k>=0} (-1/8)^(k+1) * binomial(k/9,n). - Seiichi Manyama, Aug 04 2024