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A025754 9th-order Patalan numbers (generalization of Catalan numbers). 2
1, 1, 36, 1836, 107406, 6766578, 446594148, 30432201228, 2122646035653, 150707868531363, 10850966534258136, 790147653994615176, 58075852568604215436, 4302080463351219958836, 320812285981333831216056 (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.: (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

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Last modified February 27 10:25 EST 2021. Contains 341649 sequences. (Running on oeis4.)