A025763 10th-order Vatalan numbers (generalization of Catalan numbers).

1, 1, 46, 2941, 214486, 16801306, 1376657776, 116346220021, 10057692309166, 884572748725086, 78862377561315156, 7108473985655908626, 646575307673212875996, 59260508917444358016516

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, A025760, A025761, A025762.

Programs

Mathematica

Table[SeriesCoefficient[10/(9 + (1 - 100 x)^(1/10)), {x, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Dec 29 2012 *)
CoefficientList[Series[10/(9+Surd[1-100x,10]),{x,0,20}],x] (* Harvey P. Dale, Feb 12 2017 *)

Formula

G.f.: 10/(9 + (1 - 100*x)^(1/10)).

a(n) = (-1)^(n+1) * 10^(2*n+1) * Sum_{k>=0} (-1/9)^(k+1) * binomial(k/10,n). - Seiichi Manyama, Aug 04 2024