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A248325
Square array read by antidiagonals downwards: super Patalan numbers of order 4.
5
1, 4, 12, 40, 24, 168, 480, 160, 224, 2464, 6240, 1440, 1120, 2464, 36960, 84864, 14976, 8064, 9856, 29568, 561792, 1188096, 169728, 69888, 59136, 98560, 374528, 8614144, 16972800, 2036736, 678912, 439296, 506880, 1070080, 4922368, 132903936, 246105600, 25459200, 7128576, 3734016, 3294720, 4815360
OFFSET
0,2
COMMENTS
Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 4, A025749.
LINKS
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)*(16*n-4)/(n+k), T(n,k) = T(n,k-1)*(16*k-12)/(n+k).
G.f.: (x/(1-16*x)^(3/4)+y/(1-16*y)^(1/4))/(x+y-16*x*y).
EXAMPLE
T(0..4, 0..4) is:
1 4 40 480 6240
12 24 160 1440 14976
168 224 1120 8064 69888
2464 2464 9856 59136 439296
36960 29568 98560 506880 3294720
CROSSREFS
Cf. A068555, A025749, A216702 (first column), A034385 (first row), A248324.
Sequence in context: A149330 A149331 A009532 * A344122 A328533 A265127
KEYWORD
nonn,tabl,easy,changed
AUTHOR
Tom Richardson, Oct 04 2014
STATUS
approved