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%I #5 Mar 30 2012 17:34:40
%S 1,-1,1,1,-2,1,-1,2,-3,1,1,-2,3,-4,1,-1,2,-3,4,-5,1,1,-2,3,-4,5,-6,1,
%T -1,2,-3,4,-5,6,-7,1,1,-2,3,-4,5,-6,7,-8,1,-1,2,-3,4,-5,6,-7,8,-9,1,1,
%U -2,3,-4,5,-6,7,-8,9,-10,1
%N Triangle t(n,m) read by rows: t(n,n)= 1, t(n,m) = (-1)^(n+m)*(m+1), 0<=m<n.
%C Row sums are 1, 0, 0, -1, -1, -2, -2, -3, -3, -4, -4,..
%C Obtained from A144328 by deleting the first column, adding a diagonal of +1's, and multiplication with (-1)^(n-m).
%F t(n,m) = [x^m] (x^n - sum_{j=1..n} (-1)^(j+(n mod 2)) *j*x^(j-1) ) .
%e 1;
%e -1, 1;
%e 1, -2, 1;
%e -1, 2, -3, 1;
%e 1, -2, 3, -4, 1;
%e -1, 2, -3, 4, -5, 1;
%e 1, -2, 3, -4, 5, -6, 1;
%e -1, 2, -3, 4, -5, 6, -7, 1;
%e 1, -2, 3, -4, 5, -6, 7, -8, 1;
%e -1, 2, -3, 4, -5, 6, -7, 8, -9, 1;
%e 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 1;
%t p[x, 0] = 1;
%t p[x_, n_] := p[x, n] = x^n - Sum[(-1)^(i + Mod[n, 2])*i*x^(i - 1), {i, 1, n}];
%t Table[CoefficientList[p[x, n], x], {n, 0, 10}];
%t Flatten[%]
%K sign,tabl,easy
%O 0,5
%A _Roger L. Bagula_, Apr 18 2010
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