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

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

Offset

0,3

Links

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

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

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 *)

Crossrefs

Cf. A000108, A025756, A025757, A025758, A025759, A025760, A025761, A025762.

Sequence in context: A234153 A123830 A201234 * A223884 A223891 A243648

Adjacent sequences: A025760 A025761 A025762 * A025764 A025765 A025766

Keyword

nonn

Author

Olivier Gérard

Status

approved