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A025755 10th-order Patalan numbers (generalization of Catalan numbers). 2
1, 1, 45, 2850, 206625, 16116750, 1316201250, 110936962500, 9568313015625, 839885253593750, 74749787569843750, 6727480881285937500, 611079513383472656250, 55937278532794804687500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

T. M. Richardson, The Super Patalan Numbers, arXiv preprint arXiv:1410.5880, 2014 and J. Int. Seq. 18 (2015) # 15.3.3

FORMULA

G.f.: (11-(1-100*x)^(1/10))/10.

a(n) = 10^(n-1)*9*A035278(n-1)/n!, n >= 2; 9*A035278(n-1) = (10*n-11)(!^10) = Product_{j=2..n} (10*j - 11). - Wolfdieter Lang

Conjecture: n*a(n) + 10*(-10*n+11)*a(n-1) = 0. - R. J. Mathar, Jul 28 2014

a(n) = 100^(n-1)*Pochhammer(9/10, n-1)/n! for n >= 1.  Maple confirms this satisfies Mathar's conjecture for n >= 2 (it's not true for n=1). - Robert Israel, Oct 05 2014

MATHEMATICA

CoefficientList[Series[(11 -(1 - 100*x)^(1/10))/10, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)

CROSSREFS

Sequence in context: A035097 A184286 A130017 * A213880 A113630 A143004

Adjacent sequences:  A025752 A025753 A025754 * A025756 A025757 A025758

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 27 11:24 EST 2021. Contains 341656 sequences. (Running on oeis4.)