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A025751
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6th-order Patalan numbers (generalization of Catalan numbers).
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4
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1, 1, 15, 330, 8415, 232254, 6735366, 202060980, 6213375135, 194685754230, 6191006984514, 199237861137996, 6475230486984870, 212188322111965740, 7002214629694869420, 232473525705869664744, 7758803920433400060831
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Wolfdieter 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
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FORMULA
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G.f.: (7-(1-36*x)^(1/6))/6.
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.
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MATHEMATICA
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CoefficientList[Series[(7 - (1 - 36*x)^(1/6))/6, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)
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PROG
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(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 */
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CROSSREFS
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Cf. A034787.
Sequence in context: A119296 A180779 A196666 * A027402 A053104 A114937
Adjacent sequences: A025748 A025749 A025750 * A025752 A025753 A025754
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KEYWORD
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nonn
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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