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%I #16 Aug 24 2023 09:31:08
%S 0,-1,0,-64,-3,4080,-729,-128,29515,236160,-4096,-1215,123168,986873,
%T 4194240,-15625,-6144,373899,3004544,12770391,39062400,-46656,-21875,
%U 925648,7468533,31750240,97119349,241864560,-117649,-62208,1989555,16131200,68598447,209838336,522579107,1129900800
%N Triangle, T(n, k) = k^6 - n^6 - 5*(n*k)^2*(n^2 - k^2) + 4*n*k*((n*k)^4 - 1), read by rows.
%H G. C. Greubel, <a href="/A123964/b123964.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = k^6 - n^6 - 5*n^2*k^2*(n^2 - k^2) + 4*n*k*(n^4*k^4 - 1).
%e Triangle begins as:
%e 0;
%e -1, 0;
%e -64, -3, 4080;
%e -729, -128, 29515, 236160;
%e -4096, -1215, 123168, 986873, 4194240;
%e -15625, -6144, 373899, 3004544, 12770391, 39062400;
%e -46656, -21875, 925648, 7468533, 31750240, 97119349, 241864560;
%t T[n_, m_]= m^6 -n^6 - 5*n^2*m^2*(n^2 -m^2) + 4*n*m*(n^4*m^4 -1);
%t Table[T[n,m], {n,0,12}, {m,0,n}]//Flatten
%o (Magma)
%o A123964:= func< n,k | k^6-n^6 -5*(n*k)^2*(n^2-k^2) +4*n*k*((n*k)^4-1) >;
%o [A123964(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Aug 20 2023
%o (SageMath)
%o def A123964(n,k): return k^6-n^6 -5*(n*k)^2*(n^2-k^2) +4*n*k*((n*k)^4 - 1)
%o flatten([[A123964(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Aug 20 2023
%K sign,tabl,easy
%O 0,4
%A _Roger L. Bagula_, Oct 28 2006
%E Edited by _G. C. Greubel_, Aug 20 2023
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