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

0,3

Links

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A370149 A088872 A371489 * A297313 A297505 A099807

Adjacent sequences: A025759 A025760 A025761 * A025763 A025764 A025765

Keyword

nonn

Author

Olivier Gérard

Status

approved