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

1, 1, 15, 330, 8415, 232254, 6735366, 202060980, 6213375135, 194685754230, 6191006984514, 199237861137996, 6475230486984870, 212188322111965740, 7002214629694869420, 232473525705869664744, 7758803920433400060831

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_{j=2..n} (6*j - 7). - 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