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A025752
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7th order Patalan numbers (generalization of Catalan numbers).
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3
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1, 1, 21, 637, 22295, 842751, 33429123, 1370594043, 57564949806, 2462500630590, 106872527367606, 4692675519868518, 208041948047504298, 9297874755046153626, 418404363977076913170, 18939770876029014936162
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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
W. 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.: (8-(1-49*x)^(1/7))/7.
a(n) = 7^(n-1)*6*A034833(n-1)/n!, n >= 2; 6*A034833(n-1)= (7*n-8)(!^7) = product(7*j-8, j=2..n). - Wolfdieter Lang
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MATHEMATICA
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CoefficientList[Series[(8 - (1 - 49*x)^(1/7))/7, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)
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CROSSREFS
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Sequence in context: A231852 A327681 A141265 * A163032 A209264 A012501
Adjacent sequences: A025749 A025750 A025751 * A025753 A025754 A025755
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KEYWORD
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nonn,easy
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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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