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%I #26 Jan 31 2021 22:25:13
%S 1,1,28,1120,51520,2555392,132880384,7137574912,392566620160,
%T 21983730728960,1248675905404928,71742106565083136,
%U 4161042180774821888,243260927491451125760,14317643160925409116160
%N 8th-order Patalan numbers (generalization of Catalan numbers).
%H Vincenzo Librandi, <a href="/A025753/b025753.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.: (9-(1-64*x)^(1/9))/8.
%F a(n) = 8^(n-1)*7*A034975(n-1)/n!, n >= 2; 7*A034975(n-1)= (8*n-9)!^8 = Product_{j=2..n} (8*j - 9). - _Wolfdieter Lang_
%t CoefficientList[Series[(9 - (1 - 64*x)^(1/8))/8, {x, 0, 20}], x] (* _Vincenzo Librandi_, Dec 29 2012 *)
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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