|
%I #29 Jan 31 2021 22:24:55
%S 1,1,36,1836,107406,6766578,446594148,30432201228,2122646035653,
%T 150707868531363,10850966534258136,790147653994615176,
%U 58075852568604215436,4302080463351219958836,320812285981333831216056
%N 9th-order Patalan numbers (generalization of Catalan numbers).
%H Vincenzo Librandi, <a href="/A025754/b025754.txt">Table of n, a(n) for n = 0..200</a>
%H W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LANG/lang.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%H Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H T. M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv preprint arXiv:1410.5880, 2014 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Richardson/rich2.html">J. Int. Seq. 18 (2015) # 15.3.3</a>
%F G.f.: (10-(1-81*x)^(1/9))/9.
%F 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_
%F Conjecture: n*a(n) + 9*(-9*n+10)*a(n-1) = 0. - _R. J. Mathar_, Jul 28 2014
%t CoefficientList[Series[(10-(1-81x)^(1/9))/9,{x,0,20}],x] (* _Harvey P. Dale_, Nov 29 2012 *)
%K nonn
%O 0,3
%A _Olivier Gérard_
|
