A025752 7th-order Patalan numbers (generalization of Catalan numbers).

1, 1, 21, 637, 22295, 842751, 33429123, 1370594043, 57564949806, 2462500630590, 106872527367606, 4692675519868518, 208041948047504298, 9297874755046153626, 418404363977076913170, 18939770876029014936162

Offset

0,3

Links

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

Formula

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_{j=2..n} (7*j - 8). - Wolfdieter Lang

Mathematica

CoefficientList[Series[(8 - (1 - 49*x)^(1/7))/7, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)

Crossrefs

Sequence in context: A231852 A327681 A141265 * A163032 A209264 A012501

Adjacent sequences: A025749 A025750 A025751 * A025753 A025754 A025755

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved