A025754 9th-order Patalan numbers (generalization of Catalan numbers).

1, 1, 36, 1836, 107406, 6766578, 446594148, 30432201228, 2122646035653, 150707868531363, 10850966534258136, 790147653994615176, 58075852568604215436, 4302080463351219958836, 320812285981333831216056

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.: (10-(1-81*x)^(1/9))/9.

a(n) = 9^(n-1)*8*A035022(n-1)/n!, n >= 2; 8*A035022(n-1)= (9*n-10)(!^9)= Product_{j=2..n} (9*j - 10). - Wolfdieter Lang

Conjecture: n*a(n) + 9*(-9*n+10)*a(n-1) = 0. - R. J. Mathar, Jul 28 2014

Mathematica

CoefficientList[Series[(10-(1-81x)^(1/9))/9, {x, 0, 20}], x] (* Harvey P. Dale, Nov 29 2012 *)

Crossrefs

Sequence in context: A113618 A054980 A151640 * A071128 A065782 A160482

Adjacent sequences: A025751 A025752 A025753 * A025755 A025756 A025757

Keyword

nonn

Author

Olivier Gérard

Status

approved