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).

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

Offset

1,11

Links

Table of n, a(n) for n=1..66.

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