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A248324 Square array read by antidiagonals downwards: super Patalan numbers of order 3. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

a(0,0)=1, a(n,k) = a(n-1,k)*(9*n-3)/(n+k), a(n,k) = a(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

a(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 * A078318 A193433 A074370

Adjacent sequences:  A248321 A248322 A248323 * A248325 A248326 A248327

KEYWORD

tabl,easy,nonn

AUTHOR

Tom Richardson, Oct 04 2014

STATUS

approved

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)