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A025753 8th-order Patalan numbers (generalization of Catalan numbers). 3
1, 1, 28, 1120, 51520, 2555392, 132880384, 7137574912, 392566620160, 21983730728960, 1248675905404928, 71742106565083136, 4161042180774821888, 243260927491451125760, 14317643160925409116160 (list; graph; refs; listen; history; text; internal format)
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: A228689 A218480 A162006 * A160312 A132503 A092705

Adjacent sequences:  A025750 A025751 A025752 * A025754 A025755 A025756

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 27 11:38 EST 2021. Contains 341656 sequences. (Running on oeis4.)