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A025751 6th order Patalan numbers (generalization of Catalan numbers). 4
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)
OFFSET

0,3

LINKS

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

FORMULA

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 (6*j-7, j=2..n). - Wolfdieter Lang.

MATHEMATICA

CoefficientList[Series[(7 - (1 - 36*x)^(1/6))/6, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)

PROG

(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 */

CROSSREFS

Cf. A034787.

Sequence in context: A119296 A180779 A196666 * A027402 A053104 A114937

Adjacent sequences:  A025748 A025749 A025750 * A025752 A025753 A025754

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified July 9 14:08 EDT 2020. Contains 335543 sequences. (Running on oeis4.)