A025761 - OEIS

%I #19 Aug 04 2024 12:43:30

%S 1,1,29,1177,54629,2726977,142504685,7685245225,424109499317,

%T 23818681210961,1356315674712509,78100982458201017,

%U 4538960021319997189,265837773438037013857,15672475449746510425485

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

%H Vincenzo Librandi, <a href="/A025761/b025761.txt">Table of n, a(n) for n = 0..200</a>

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

%F 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

%t Table[SeriesCoefficient[8/(7 + (1 - 64 x)^(1/8)), {x, 0, n}], {n, 0, 20}] (* _Vincenzo Librandi_, Dec 29 2012 *)

%t CoefficientList[Series[8/(7+Surd[1-64x,8]),{x,0,20}],x] (* _Harvey P. Dale_, Jun 19 2022 *)

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

%K nonn

%O 0,3

%A _Olivier Gérard_