A025760 7th-order Vatalan numbers (generalization of Catalan numbers).

1, 1, 22, 680, 24074, 917414, 36618492, 1508943612, 63643109727, 2732349490669, 118957846271104, 5237911268468572, 232794783971436296, 10427673857731312064, 470213556090357498728, 21325335129901497816528

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, A025761, A025762, A025763.

Programs

Mathematica

Table[SeriesCoefficient[7/(6 + (1 - 49*x)^(1/7)), {x, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Dec 29 2012 *)

Formula

G.f.: 7/(6 + (1 - 49*x)^(1/7)).

a(n) = (-1)^(n+1) * 7^(2*n+1) * Sum_{k>=0} (-1/6)^(k+1) * binomial(k/7,n). - Seiichi Manyama, Aug 04 2024