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%I #30 Jan 31 2021 21:50:14
%S 1,1,15,330,8415,232254,6735366,202060980,6213375135,194685754230,
%T 6191006984514,199237861137996,6475230486984870,212188322111965740,
%U 7002214629694869420,232473525705869664744,7758803920433400060831
%N 6th-order Patalan numbers (generalization of Catalan numbers).
%H Vincenzo Librandi, <a href="/A025751/b025751.txt">Table of n, a(n) for n = 0..200</a>
%H Wolfdieter 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.: (7-(1-36*x)^(1/6))/6.
%F a(n) = 6^(n-1)*5*A034787(n-1)/n!, n >= 2, 5*A034787(n-1)=(6*n-7)(!^6) := Product_{j=2..n} (6*j - 7). - _Wolfdieter Lang_.
%t CoefficientList[Series[(7 - (1 - 36*x)^(1/6))/6, {x, 0, 20}], x] (* _Vincenzo Librandi_, Dec 29 2012 *)
%o (Maxima) a[0]:1$ a[1]:1$ a[n]:=(6/n)*(6*n-7)*a[n-1]$ makelist(a[n],n,0,1000); /* _Tani Akinari_, Aug 03 2014 */
%Y Cf. A034787.
%K nonn
%O 0,3
%A _Olivier Gérard_
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