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A228832 Triangle defined by T(n,k) = binomial(n*k, k^2), for n>=0, k=0..n, as read by rows.

%I A228832 #17 Sep 22 2013 14:26:40
%S A228832 1,1,1,1,2,1,1,3,15,1,1,4,70,220,1,1,5,210,5005,4845,1,1,6,495,48620,
%T A228832 735471,142506,1,1,7,1001,293930,30421755,183579396,5245786,1,1,8,
%U A228832 1820,1307504,601080390,40225345056,69668534468,231917400,1,1,9,3060,4686825,7307872110,3169870830126,96926348578605,37387265592825,11969016345,1
%N A228832 Triangle defined by T(n,k) = binomial(n*k, k^2), for n>=0, k=0..n, as read by rows.
%C A228832 Central coefficients are A201555(n) = C(2*n^2,n^2) = A000984(n^2), where A000984 is the central binomial coefficients.
%H A228832 Paul D. Hanna, <a href="/A228832/b228832.txt">Rows 0..30, as a flattened table of n, a(n) for n = 0..495</a>
%e A228832 The triangle of coefficients C(n*k, k^2), n>=k, k=0..n, begins:
%e A228832 1;
%e A228832 1, 1;
%e A228832 1, 2, 1;
%e A228832 1, 3, 15, 1;
%e A228832 1, 4, 70, 220, 1;
%e A228832 1, 5, 210, 5005, 4845, 1;
%e A228832 1, 6, 495, 48620, 735471, 142506, 1;
%e A228832 1, 7, 1001, 293930, 30421755, 183579396, 5245786, 1;
%e A228832 1, 8, 1820, 1307504, 601080390, 40225345056, 69668534468, 231917400, 1;
%e A228832 1, 9, 3060, 4686825, 7307872110, 3169870830126, 96926348578605, 37387265592825, 11969016345, 1; ...
%o A228832 (PARI) {T(n, k)=binomial(n*k, k^2)}
%o A228832 for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
%Y A228832 Cf. A228808 (row sums), A228833 (antidiagonal sums), A135860 (diagonal), A201555 (central terms).
%Y A228832 Cf. A229052.
%Y A228832 Cf. related triangles: A228904 (exp), A209330, A226234, A228836.
%K A228832 nonn,tabl
%O A228832 0,5
%A A228832 _Paul D. Hanna_, Sep 04 2013