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A226234 Triangle defined by T(n,k) = binomial(n^2, k^2), for n>=0, k=0..n, as read by rows. 6

%I

%S 1,1,1,1,4,1,1,9,126,1,1,16,1820,11440,1,1,25,12650,2042975,2042975,1,

%T 1,36,58905,94143280,7307872110,600805296,1,1,49,211876,2054455634,

%U 3348108992991,63205303218876,262596783764,1,1,64,635376,27540584512,488526937079580,401038568751465792,1118770292985239888,159518999862720,1

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

%C Row sums equal A206849.

%C Antidiagonal sums equal A123165.

%H Paul D. Hanna, <a href="/A226234/b226234.txt">Rows n = 0..30, as a flattened table of n, a(n) for n = 0..495</a>

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

%e 1;

%e 1, 1;

%e 1, 4, 1;

%e 1, 9, 126, 1;

%e 1, 16, 1820, 11440, 1;

%e 1, 25, 12650, 2042975, 2042975, 1;

%e 1, 36, 58905, 94143280, 7307872110, 600805296, 1;

%e 1, 49, 211876, 2054455634, 3348108992991, 63205303218876, 262596783764, 1;

%e 1, 64, 635376, 27540584512, 488526937079580, 401038568751465792, 1118770292985239888, 159518999862720, 1; ...

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

%o for(n=0,9,for(k=0,n,print1(T(n,k),", "));print(""))

%Y Cf. A206849, A123165.

%Y Cf. related triangles: A228902(exp), A209330, A228832, A228836.

%K nonn,tabl

%O 0,5

%A _Paul D. Hanna_, Aug 24 2013

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Last modified February 21 18:05 EST 2020. Contains 332107 sequences. (Running on oeis4.)