A248324 - OEIS

A248324

Square array read by antidiagonals downwards: super Patalan numbers of order 3.

1, 3, 6, 18, 9, 45, 126, 36, 45, 360, 945, 189, 135, 270, 2970, 7371, 1134, 567, 648, 1782, 24948, 58968, 7371, 2835, 2268, 3564, 12474, 212058, 480168, 50544, 15795, 9720, 10692, 21384, 90882, 1817640, 3961386, 360126, 94770, 47385, 40095, 56133, 136323, 681615, 15677145, 33011550, 2640924, 600210, 252720, 173745, 187110, 318087, 908820, 5225715, 135868590

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OFFSET

0,2

COMMENTS

Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 3, A097188.

LINKS

Table of n, a(n) for n=0..54.

Thomas M. Richardson, The Super Patalan Numbers, arXiv:1410.5880 [math.CO], 2014.

Thomas M. Richardson, The Super Patalan Numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.3.

FORMULA

T(0,0)=1, T(n,k) = T(n-1,k)*(9*n-3)/(n+k), T(n,k) = T(n,k-1)*(9*k-6)/(n+k).

G.f.: (x/(1-9*x)^(2/3)+y/(1-9*y)^(1/3))/(x+y-9*x*y).

EXAMPLE

T(0..4,0..4) is:

1 3 18 126 945

6 9 36 189 1134

45 45 135 567 2835

360 270 648 2268 9720

2970 1782 3564 10692 40095

CROSSREFS

Cf. A068555, A248325. First column is A004988, first row is A004987. a(n,1) = -A004990(n+1) = 3*A097188(n). a(1,k) = -A004989(k+1).

Sequence in context: A106158 A274103 A195995 * A341119 A078318 A193433

Adjacent sequences: A248321 A248322 A248323 * A248325 A248326 A248327

KEYWORD

tabl,easy,nonn,changed

AUTHOR

Tom Richardson, Oct 04 2014

STATUS

approved