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%I #27 Jan 31 2021 22:24:33
%S 1,1,21,637,22295,842751,33429123,1370594043,57564949806,
%T 2462500630590,106872527367606,4692675519868518,208041948047504298,
%U 9297874755046153626,418404363977076913170,18939770876029014936162
%N 7th-order Patalan numbers (generalization of Catalan numbers).
%H Vincenzo Librandi, <a href="/A025752/b025752.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.: (8-(1-49*x)^(1/7))/7.
%F a(n) = 7^(n-1)*6*A034833(n-1)/n!, n >= 2; 6*A034833(n-1)= (7*n-8)(!^7) = Product_{j=2..n} (7*j - 8). - _Wolfdieter Lang_
%t CoefficientList[Series[(8 - (1 - 49*x)^(1/7))/7, {x, 0, 20}], x] (* _Vincenzo Librandi_, Dec 29 2012 *)
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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