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A334702 Array read by antidiagonals: T(n,k) = binomial(n*k,3), n>=0, k>=0.

%I A334702 #19 Jun 14 2020 05:46:29
%S A334702 0,0,0,0,0,0,0,0,0,0,0,1,4,1,0,0,4,20,20,4,0,0,10,56,84,56,10,0,0,20,
%T A334702 120,220,220,120,20,0,0,35,220,455,560,455,220,35,0,0,56,364,816,1140,
%U A334702 1140,816,364,56,0,0,84,560,1330,2024,2300,2024,1330,560,84,0,0,120,816,2024,3276,4060,4060,3276,2024,816,120
%N A334702 Array read by antidiagonals: T(n,k) = binomial(n*k,3), n>=0, k>=0.
%e A334702 The initial rows of the array are:
%e A334702 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
%e A334702 [0, 0, 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455]
%e A334702 [0, 0, 4, 20, 56, 120, 220, 364, 560, 816, 1140, 1540, 2024, 2600, 3276, 4060]
%e A334702 [0, 1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060, 5456, 7140, 9139, 11480, 14190]
%e A334702 [0, 4, 56, 220, 560, 1140, 2024, 3276, 4960, 7140, 9880, 13244, 17296, 22100, 27720, 34220]
%e A334702 [0, 10, 120, 455, 1140, 2300, 4060, 6545, 9880, 14190, 19600, 26235, 34220, 43680, 54740, 67525]
%e A334702 [0, 20, 220, 816, 2024, 4060, 7140, 11480, 17296, 24804, 34220, 45760, 59640, 76076, 95284, 117480]
%e A334702 [0, 35, 364, 1330, 3276, 6545, 11480, 18424, 27720, 39711, 54740, 73150, 95284 , 121485, 152096, 187460]
%e A334702 [0, 56, 560, 2024, 4960, 9880, 17296, 27720, 41664, 59640, 82160, 109736, 142880, 182104, 227920, 280840]
%e A334702 ...
%e A334702 The first few antidiagonals are:
%e A334702 [0]
%e A334702 [0, 0]
%e A334702 [0, 0, 0]
%e A334702 [0, 0, 0, 0]
%e A334702 [0, 1, 4, 1, 0]
%e A334702 [0, 4, 20, 20, 4, 0]
%e A334702 [0, 10, 56, 84, 56, 10, 0]
%e A334702 [0, 20, 120, 220, 220, 120, 20, 0]
%e A334702 [0, 35, 220, 455, 560, 455, 220, 35, 0]
%e A334702 [0, 56, 364, 816, 1140, 1140, 816, 364, 56, 0]
%e A334702 [0, 84, 560, 1330, 2024, 2300, 2024, 1330, 560, 84, 0]
%e A334702 ...
%Y A334702 Cf. A007318.
%Y A334702 See A334703 for the entries on or below the main diagonal displayed as a triangle.
%K A334702 nonn,tabl
%O A334702 0,13
%A A334702 _N. J. A. Sloane_, Jun 13 2020