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%I #5 Nov 05 2012 19:39:30
%S 1,1,1,1,-8,1,1,-103,-103,1,1,-644,-4284,-644,1,1,-3199,-91004,-91004,
%T -3199,1,1,-14328,-1418031,-5836256,-1418031,-14328,1,1,-60911,
%U -18428967,-243950711,-243950711,-18428967,-60911,1,1,-251876
%N Triangle t(n, m) = 2*binomial(n,m)^2 -A008292(n+1,m+1)^2 read by rows.
%C Row sums are A028329(n) - A168562(n+1). - _R. J. Mathar_, Nov 05 2012
%e 1;
%e 1, 1;
%e 1, -8, 1;
%e 1, -103, -103, 1;
%e 1, -644, -4284, -644, 1;
%e 1, -3199, -91004, -91004, -3199, 1;
%e 1, -14328, -1418031, -5836256, -1418031, -14328, 1;
%e 1, -60911, -18428967, -243950711, -243950711, -18428967, -60911, 1;
%e 1, -251876, -213392096, -7785232484, -24395306300, -7785232484, -213392096, -251876, 1;
%t << DiscreteMath`Combinatorica`
%t t[n_, m_] = 2*Binomial[n, m]^2 - Eulerian[n + 1, m]^2;
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%Y Cf. A177823, A008459, A141686, A008292
%K sign,tabl
%O 0,5
%A _Roger L. Bagula_, May 18 2010