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 A123730 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). 0
 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, 0, -1, 57, -10, 46, -69, -13, 19, 0, -1, 35, 37, 113, 150, -160, -19, 26, 0, -1, -533, 129, -478, 609, 345, -312, -26, 34, 0, -1, 141, -946, -520, -2380, 1945, 668, -546, -34, 43, 0, -1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 LINKS EXAMPLE Triangular sequence: {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, 0, -1}, {57, -10, 46, -69, -13,19, 0, -1}, {35, 37, 113, 150, -160, -19, 26, 0, -1}, {-533, 129, -478, 609, 345, -312, -26, 34, 0, -1}, {141, -946, -520, -2380, 1945, 668, -546, -34, 43, 0, -1} MAPLE 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 MATHEMATICA 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] CROSSREFS Sequence in context: A119719 A125162 A174382 * A143317 A130540 A076816 Adjacent sequences:  A123727 A123728 A123729 * A123731 A123732 A123733 KEYWORD sign,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Nov 14 2006 EXTENSIONS Edited by N. J. A. Sloane, Dec 03 2006 STATUS approved

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