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Triangle read by rows: T(n,k) = binomial(n,k)^2 * binomial(2*(n-k), n-k).
1

%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