A228836 - OEIS

%I #11 Sep 08 2013 17:32:40

%S 1,1,1,1,4,1,1,36,36,1,1,560,1820,560,1,1,12650,177100,177100,12650,1,

%T 1,376992,30260340,94143280,30260340,376992,1,1,13983816,8217822536,

%U 92263734836,92263734836,8217822536,13983816,1,1,621216192,3284214703056,159518999862720,488526937079580

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

%H Paul D. Hanna, <a href="/A228836/b228836.txt">Rows 0..30 as a flattened table of n, a(n) for n = 0..495</a>

%e The triangle of coefficients C(n^2, (n-k)*k), n>=k, k=0..n, begins:

%e 1;

%e 1, 1;

%e 1, 4, 1;

%e 1, 36, 36, 1;

%e 1, 560, 1820, 560, 1;

%e 1, 12650, 177100, 177100, 12650, 1;

%e 1, 376992, 30260340, 94143280, 30260340, 376992, 1;

%e 1, 13983816, 8217822536, 92263734836, 92263734836, 8217822536, 13983816, 1;

%e 1, 621216192, 3284214703056, 159518999862720, 488526937079580, 159518999862720, 3284214703056, 621216192, 1; ...

%o (PARI) {T(n,k)=binomial(n^2, (n-k)*k)}

%o for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

%Y Cf. A207136 (row sums), A228837 (antidiagonal sums), A070780 (column 1).

%Y Cf. related triangles: A228900(exp), A209330, A226234, A228832.

%K nonn,tabl

%O 0,5

%A _Paul D. Hanna_, Sep 05 2013