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%I #14 Dec 10 2023 17:34:22
%S 1,1,1,1,4,2,1,9,12,4,1,16,42,34,8,1,25,110,160,90,16,1,36,240,550,
%T 540,226,32,1,49,462,1540,2310,1666,546,64,1,64,812,3724,7910,8596,
%U 4802,1282,128,1,81,1332,8064,23058,34986,29190,13140,2946,256
%N Triangle read by rows: T(n,m)= Sum_{k=0..m/2} C(n-k,m-2*k)*C(n-k,m-k)*C(n,k)/C(2*k,k).
%F G.f.: A008459(x,y)/(1-(x*y*A008459(x,y))^2).
%e 1,
%e 1, 1,
%e 1, 4, 2,
%e 1, 9, 12, 4,
%e 1, 16, 42, 34, 8,
%e 1, 25, 110, 160, 90, 16,
%e 1, 36, 240, 550, 540, 226, 32
%o (Maxima)
%o T(n,m):=sum((binomial(n-k,m-2*k)*binomial(n-k,m-k)*binomial(n,k))/binomial(2*k,k) ,k,0,m/2);
%Y Cf. A001263, A008459, A176280 (row sums), A338372.
%K nonn,tabl
%O 0,5
%A _Vladimir Kruchinin_, Oct 23 2020
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