%I #9 Aug 25 2018 21:20:40
%S 1,2,1,6,8,1,20,54,18,1,70,320,216,32,1,252,1750,2000,600,50,1,924,
%T 9072,15750,8000,1350,72,1,3432,45276,111132,85750,24500,2646,98,1,
%U 12870,219648,724416,790272,343000,62720,4704,128,1,48620,1042470,4447872,6519744,4000752,1111320,141120,7776,162,1
%N Triangle read by rows: T(n,k) = binomial(n,k)^2 * binomial(2*(n-k), n-k).
%C The square of the triangular matrix {binomial(n, k)^2}_{k=0..n} A008459 read by rows.
%e Triangle begins:
%e 1
%e 2 1
%e 6 8 1
%e 20 54 18 1
%e 70 320 216 32 1
%e ...
%t T[ n_, k_] := Binomial[n, k]^2 Binomial[2 n - 2 k, n - k];
%o (PARI) {T(n, k) = binomial(n, k)^2 * binomial(2*(n-k), n-k)};
%Y Row sums give A002893.
%Y Cf. A008459.
%K nonn,tabl,easy
%O 0,2
%A _Michael Somos_, Aug 25 2018