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%I #3 Oct 12 2012 14:54:52
%S -1,-1,-1,-1,-1,0,-1,-1,-1,0,-1,0,-1,-1,-1,0,-1,0,-1,0,-1,-1,-1,0,-1,
%T 0,-1,0,-1,0,-1,-1,-1,0,-1,0,-1,0,-1,0,-1,0,-1,-1,-1,0,-1,0,-1,0,-1,0,
%U -1,0,-1,0,-1,-1,-1,0,-1,0,-1,0,-1,0,-1,0,-1,0,-1,0,-1,-1,-1,0,-1,0,-1,0,-1,0,-1,0,-1,0,-1,0,-1,0,-1
%N A triangle sequence of coefficients of odd sum polynomials: p(x,n)=x^(2*n - 1) - Sum[x^(2*i + 1), {i, 0, n - 1}] - 1.
%C Row sums are:
%C {-1, -2, -3, -4, -5, -6, -7, -8, -9, -10}.
%F p(x,n)=x^(2*n - 1) - Sum[x^(2*i + 1), {i, 0, n - 1}] - 1; t(n,m)=coefficients(p)x,n).
%e {-1},
%e {-1, -1},
%e {-1, -1, 0, -1},
%e {-1, -1, 0, -1, 0, -1},
%e {-1, -1, 0, -1, 0, -1, 0, -1},
%e {-1, -1, 0, -1, 0, -1, 0, -1, 0, -1},
%e {-1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1},
%e {-1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1},
%e {-1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1},
%e {-1, -1, 0, -1, 0, -1, 0, -1, 0, -1,0, -1, 0, -1, 0, -1, 0, -1}
%t p[x_, n_] := x^(2*n - 1) - Sum[x^(2*i + 1), {i, 0, n - 1}] - 1; Table[Expand[p[x, n]], {n, 1, 10}]; Table[CoefficientList[p[x, n], x], {n, 1, 10}]; Flatten[%] b = Table[Apply[Plus, Re[CoefficientList[p[x, n], x]]], {n, 1, 10}]
%K uned,sign
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 27 2008