A025761 8th-order Vatalan numbers (generalization of Catalan numbers).

1, 1, 29, 1177, 54629, 2726977, 142504685, 7685245225, 424109499317, 23818681210961, 1356315674712509, 78100982458201017, 4538960021319997189, 265837773438037013857, 15672475449746510425485

Offset

0,3

Links

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

Formula

G.f.: 8/(7 + (1 - 64*x)^(1/8)).

a(n) = (-1)^(n+1) * 8^(2*n+1) * Sum_{k>=0} (-1/7)^(k+1) * binomial(k/8,n). - Seiichi Manyama, Aug 04 2024

Mathematica

Table[SeriesCoefficient[8/(7 + (1 - 64 x)^(1/8)), {x, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Dec 29 2012 *)
CoefficientList[Series[8/(7+Surd[1-64x, 8]), {x, 0, 20}], x] (* Harvey P. Dale, Jun 19 2022 *)

Crossrefs

Cf. A000108, A025756, A025757, A025758, A025759, A025760, A025762, A025763.

Sequence in context: A176695 A210303 A268461 * A003735 A159479 A264351

Adjacent sequences: A025758 A025759 A025760 * A025762 A025763 A025764

Keyword

nonn

Author

Olivier Gérard

Status

approved