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%I #23 Apr 25 2015 11:22:42
%S 1,5,20,75,50,450,1375,500,750,10500,27500,6875,5625,13125,249375,
%T 577500,110000,61875,78750,249375,5985000,12512500,1925000,825000,
%U 721875,1246875,4987500,144637500,277062500,35750000,12375000,8250000,9796875,21375000,103312500,3512625000,6233906250,692656250
%N Square array read by antidiagonals downward: super Patalan numbers of order 5.
%C Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 5, A025750.
%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 a(0,0)=1, a(n,k) = a(n-1,k)*(25*n-5)/(n+k), a(n,k) = a(n,k-1)*(25*k-20)/(n+k).
%F G.f.: ((x/(1-25*x)^(4/5)+y/(1-25*y)^(1/5))/(x+y-25*x*y).
%F a(n,k) = (-1)^k*25^(n+k)*binomial(n-1/5,n+k).
%e a(0..4,0..4) is
%e 1 5 75 1375 27500
%e 20 50 500 6875 110000
%e 450 750 5625 61875 825000
%e 10500 13125 78750 721875 8250000
%e 249375 249375 1246875 9796875 97968750
%o (PARI) matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*25^(n+k)*binomial(n-1/5,n+k)) \\ _Michel Marcus_, Oct 09 2014
%Y Cf. A068555, A025750, A034688 (first row), A049382 (first column), A248324, A248325, A248328, A248329, A248332.
%K nonn,easy,tabl
%O 0,2
%A _Tom Richardson_, Oct 04 2014
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