A025753 8th-order Patalan numbers (generalization of Catalan numbers).

1, 1, 28, 1120, 51520, 2555392, 132880384, 7137574912, 392566620160, 21983730728960, 1248675905404928, 71742106565083136, 4161042180774821888, 243260927491451125760, 14317643160925409116160

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.: (9-(1-64*x)^(1/9))/8.

a(n) = 8^(n-1)*7*A034975(n-1)/n!, n >= 2; 7*A034975(n-1)= (8*n-9)!^8 = Product_{j=2..n} (8*j - 9). - Wolfdieter Lang

Mathematica

CoefficientList[Series[(9 - (1 - 64*x)^(1/8))/8, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)

Crossrefs

Sequence in context: A162006 A365029 A370358 * A160312 A132503 A092705

Adjacent sequences: A025750 A025751 A025752 * A025754 A025755 A025756

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved