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%I #6 Sep 11 2013 17:50:30
%S 1,1,1,1,7,1,1,17,17,1,1,31,71,31,1,1,49,199,199,49,1,1,71,449,799,
%T 449,71,1,1,97,881,2449,2449,881,97,1,1,127,1567,6271,9799,6271,1567,
%U 127,1,1,161,2591,14111,31751,31751,14111,2591,161,1,1,199,4049,28799,88199
%N Triangle T(n,k) = 2*binomial(n,k)^2-1, read by rows, 0<=k<=n.
%C Row sums are 1, 2, 9, 36, 135, 498, 1841, 6856, 25731, 97230, 369501,... = 2*binomial(2n,n)-(n+1) = A134759(n).
%e 1;
%e 1, 1;
%e 1, 7, 1;
%e 1, 17, 17, 1;
%e 1, 31, 71, 31, 1;
%e 1, 49, 199, 199, 49, 1;
%e 1, 71, 449, 799, 449, 71, 1;
%e 1, 97, 881, 2449, 2449, 881, 97, 1;
%e 1, 127, 1567, 6271, 9799, 6271, 1567, 127, 1;
%e 1, 161, 2591, 14111, 31751, 31751, 14111, 2591, 161, 1;
%e 1, 199, 4049, 28799, 88199, 127007, 88199, 28799, 4049, 199, 1;
%t Clear[t, n, m, k, l] t[n_, m_, k_, l_] := (1 + l)*Binomial[n, m]^k - l; k = 2; l = 1; Table[Table[t[n, m, k, l], {m, 0, n}], {n, 0, 10}]; Flatten[%]
%Y Cf. A141596.
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 21 2008
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