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%I #5 Oct 12 2012 14:55:30
%S 1,0,-1,-1,0,-1,1,1,0,-1,3,-1,4,0,-1,-7,-1,-4,8,0,-1,-11,2,-21,-8,13,
%T 0,-1,57,-10,46,-69,-13,19,0,-1,35,37,113,150,-160,-19,26,0,-1,-533,
%U 129,-478,609,345,-312,-26,34,0,-1,141,-946,-520,-2380,1945,668,-546,-34,43,0,-1
%N Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial p[n,x] defined by p[ -1,x]=0, p[0,x]=1, p[1,x]=-x, p[n,x]=x*p[n-1,x]-(n-1)*p[n- 2,x]+(n-2)*p[n-3,x] for n>=2 (0<=k<=n).
%e Triangular sequence:
%e {1},
%e {0, -1},
%e {-1, 0, -1},
%e {1, 1, 0, -1},
%e {3, -1, 4, 0, -1},
%e {-7, -1, -4, 8, 0, -1},
%e {-11, 2, -21, -8, 13, 0, -1},
%e {57, -10, 46, -69, -13,19, 0, -1},
%e {35, 37, 113, 150, -160, -19, 26, 0, -1},
%e {-533, 129, -478, 609, 345, -312, -26, 34, 0, -1},
%e {141, -946, -520, -2380, 1945, 668, -546, -34, 43, 0, -1}
%p p[ -1]:=0: p[0]:=1: p[1]:=-x: for n from 2 to 10 do p[n]:=sort(expand(x*p[n-1]-(n-1)*p[n-2]+(n-2)*p[n-3])) od: for n from 0 to 10 do seq(coeff(p[n],x,k),k=0..n) od; # yields sequence in triangular form
%t p[ -1, x] = 0; p[0, x] = 1; p[1, x] = -x; p[k_, x_] := p[k, x] = x*p[k - 1, x] - (k - 1)*p[k - 2, x] + (k - 2)*p[k - 3, x]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
%K sign,tabl
%O 1,11
%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 14 2006
%E Edited by _N. J. A. Sloane_, Dec 03 2006
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