%I #3 Mar 30 2012 17:34:26
%S 1,-1,1,0,-1,-1,0,0,1,-2,0,0,0,2,1,0,0,0,0,-1,4,0,0,0,0,0,-4,0,0,0,0,
%T 0,0,0,-7,0,0,0,0,0,0,0,7,-3,0,0,0,0,0,0,0,0,3,11,0,0,0,0,0,0,0,0,0,
%U -11,10,0,0,0,0,0,0,0,0,0,0,-10,-15,0,0,0,0,0,0,0,0,0,0,0,15,-24,0,0,0,0,0,0,0,0,0,0,0,0,24,16,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Triangular sequence from coefficients of a polynomial recursion: p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3).
%C Row sums are:
%C {1, 0, -2, -1, 3, 3, -4, -7, 4, 14, -1, -25, -9, 40, 33, -56}
%F p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3).
%e {1},
%e {-1, 1},
%e {0, -1, -1},
%e {0, 0, 1, -2},
%e {0, 0, 0, 2, 1},
%e {0, 0, 0, 0, -1, 4},
%e {0, 0, 0, 0, 0, -4},
%e {0, 0, 0, 0, 0, 0, 0, -7},
%e {0, 0, 0, 0, 0, 0, 0, 7, -3},
%e {0, 0, 0, 0, 0, 0, 0, 0, 3, 11},
%e {0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10},
%e {0, 0, 0, 0, 0,0, 0, 0, 0, 0, -10, -15},
%e {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,15, -24},
%e {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 16},
%e {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 49},
%e {0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, -49, -7}
%t Clear[p, x, a0, b0] p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x - 1; p[x_, n_] := p[x, n] = x*p[x, n - 1] - 2*x^2*p[x, n - 2] + x^3*p[x, n - 3]; g = Table[ExpandAll[p[x, n]], {n, 0, 15}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 15}]; Flatten[a]
%K uned,tabl,sign
%O 1,10
%A _Roger L. Bagula_, Apr 08 2008