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%I #5 Mar 30 2012 17:34:40
%S 1,1,1,1,2,1,1,1,1,1,1,-6,-14,-6,1,1,-32,-87,-87,-32,1,1,-120,-363,
%T -484,-363,-120,1,1,-415,-1339,-2067,-2067,-1339,-415,1,1,-1414,-4742,
%U -7942,-9230,-7942,-4742,-1414,1,1,-4844,-16643,-29240,-36992,-36992,-29240
%N Triangle T(n,m)= binomial(2*n,m) + binomial(2*n,n-m) -binomial(2*n,n) read by rows.
%C Row sums are 1, 2, 4, 4, -24, -236, -1448, -7640, -37424, -175436,... = 2*A032443(n) -A037965(n+1).
%F T(n,m) = T(n,n-m).
%e The triangle starts in row n=0 with columns 0<=m<=n as:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 1, 1, 1;
%e 1, -6, -14, -6, 1;
%e 1, -32, -87, -87, -32, 1;
%e 1, -120, -363, -484, -363, -120, 1;
%e 1, -415, -1339, -2067, -2067, -1339, -415, 1;
%e 1, -1414, -4742, -7942, -9230, -7942, -4742, -1414, 1;
%e 1, -4844, -16643, -29240, -36992, -36992, -29240, -16643, -4844, 1;
%e 1, -16776, -58596, -106096, -141151, -153748, -141151, -106096, -58596, -16776, 1;
%p A176564 := proc(n,m) binomial(2*n,m)+binomial(2*n,n-m) -binomial(2*n,n) ; end proc:
%t t[n_, m_] = Binomial[2*n, m] + Binomial[2*n, n - m] - (Binomial[2*n, 0] + Binomial[2*n, n]) + 1;
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K sign,tabl,easy
%O 0,5
%A _Roger L. Bagula_, Apr 20 2010
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