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%I #8 Dec 03 2016 12:18:29
%S 1,2,1,3,5,1,4,14,10,1,5,30,46,17,1,6,55,146,117,26,1,7,91,371,517,
%T 251,37,1,8,140,812,1742,1476,478,50,1,9,204,1596,4878,6376,3614,834,
%U 65,1,10,285,2892,11934,22252,19490,7890,1361,82,1,11,385,4917,26334,66352
%N Number triangle of sums of squared binomial coefficients.
%C Alternatively, number square T(n,k) = Sum_{i=0..n} binomial(i+k,k)^2 read by antidiagonals. Columns include A000027, A000330, A024166, A086020, A086023, A086025. Row sums are A006134. Diagonal sums are A110198.
%F Number triangle T(n,k) = Sum_{i=0..n-k} binomial(i+k,k)^2.
%e Rows start
%e 1;
%e 2, 1;
%e 3, 5, 1;
%e 4, 14, 10, 1;
%e 5, 30, 46, 17, 1;
%e 6, 55, 146, 117, 26, 1;
%o (PARI) T(n,k) = sum(i=0, n-k, binomial(i+k,k)^2);
%o tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print();); \\ _Michel Marcus_, Dec 03 2016
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Jul 15 2005
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