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

0,3

Links

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

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

Mathematica

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

Crossrefs

Cf. A000108, A025756, A025757, A025758, A025759, A025761, A025762, A025763.

Sequence in context: A230836 A137262 A300137 * A229124 A262417 A027409

Adjacent sequences: A025757 A025758 A025759 * A025761 A025762 A025763

Keyword

nonn

Author

Olivier Gérard

Status

approved