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Square array read by antidiagonals downwards: super Patalan numbers of order 4.
5

%I #26 Nov 11 2024 03:57:02

%S 1,4,12,40,24,168,480,160,224,2464,6240,1440,1120,2464,36960,84864,

%T 14976,8064,9856,29568,561792,1188096,169728,69888,59136,98560,374528,

%U 8614144,16972800,2036736,678912,439296,506880,1070080,4922368,132903936,246105600,25459200,7128576,3734016,3294720,4815360

%N Square array read by antidiagonals downwards: super Patalan numbers of order 4.

%C Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 4, A025749.

%H Thomas M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv:1410.5880 [math.CO], 2014.

%H Thomas M. Richardson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Richardson/rich2.html">The Super Patalan Numbers</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.3.

%F 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).

%F G.f.: (x/(1-16*x)^(3/4)+y/(1-16*y)^(1/4))/(x+y-16*x*y).

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

%e 1 4 40 480 6240

%e 12 24 160 1440 14976

%e 168 224 1120 8064 69888

%e 2464 2464 9856 59136 439296

%e 36960 29568 98560 506880 3294720

%Y Cf. A068555, A025749, A216702 (first column), A034385 (first row), A248324.

%K nonn,tabl,easy

%O 0,2

%A _Tom Richardson_, Oct 04 2014