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%I #7 Sep 08 2022 08:45:41
%S 1,1,1,1,4,1,1,9,36,1,1,16,276,560,1,1,25,1225,19600,12650,1,1,36,
%T 4005,280840,2555190,376992,1,1,49,10731,2421090,146475945,534017484,
%U 13983816,1,1,64,24976,14885696,4053946260,147055790784,163995687856,621216192,1
%N Triangle, read by rows, T(n, k) = binomial(n*binomial(n, k), k).
%C Row sums are: {1, 2, 6, 47, 854, 33502, 3217065, 696909117, 315741551830, 339451781249846, 856885032450030756, ...}.
%H G. C. Greubel, <a href="/A157108/b157108.txt">Rows n = 0..50 of triangle, flattened</a>
%F T(n, k) = binomial(n*binomial(n, k), k).
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 9, 36, 1;
%e 1, 16, 276, 560, 1;
%e 1, 25, 1225, 19600, 12650, 1;
%e 1, 36, 4005, 280840, 2555190, 376992, 1;
%e 1, 49, 10731, 2421090, 146475945, 534017484, 13983816, 1;
%p seq(seq( binomial(n*binomial(n, k), k), k=0..n), n=0..10); # _G. C. Greubel_, Nov 30 2019
%t Table[Binomial[n*Binomial[n, k], k], {n,0,10}, {k,0,n}]//Flatten
%o (PARI) T(n, k) = binomial(n*binomial(n, k), k); \\ _G. C. Greubel_, Nov 30 2019
%o (Magma) [Binomial(n*Binomial(n, k), k): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Nov 30 2019
%o (Sage) [[binomial(n*binomial(n, k), k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Nov 30 2019
%o (GAP) Flat(List([0..10], n-> List([0..n], k-> Binomial(n*Binomial(n, k), k) ))); # _G. C. Greubel_, Nov 30 2019
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Feb 23 2009
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