A123230 - OEIS

%I #7 Mar 12 2014 16:37:01

%S 1,1,1,-1,1,1,1,0,1,1,1,0,-1,1,1,1,1,1,0,1,1,-1,1,2,0,-1,1,1,1,0,2,2,

%T 1,0,1,1,1,0,-2,2,3,0,-1,1,1,1,1,2,0,3,3,1,0,1,1,-1,1,3,0,-3,3,4,0,-1,

%U 1,1

%N Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial p(n,x) defined by p(0,x)=1, p(1,x)=1+x, p(n,x)=xp(n-1,x)+(-1)^(n+1)p(n-2,x) for n>=2.

%e {1},

%e {1, 1},

%e {-1, 1, 1},

%e {1, 0, 1, 1},

%e {1, 0, -1, 1, 1},

%e {1, 1, 1, 0, 1, 1},

%e {-1, 1, 2, 0, -1, 1, 1},

%e {1, 0, 2, 2, 1, 0, 1, 1},

%e {1, 0, -2, 2, 3, 0, -1, 1,1},

%e {1, 1, 2, 0, 3, 3, 1, 0, 1, 1},

%e {-1, 1, 3, 0, -3, 3, 4, 0, -1, 1, 1}

%p P[0]:=1: P[1]:=1+x: for n from 2 to 14 do P[n]:=sort(expand(x*P[n-1]+(-1)^(n+1)*P[n-2])) od: for n from 0 to 14 do seq(coeff(P[n],x,k),k=0..n) od; # yields sequence in triangular form

%t p[0, x] = 1; p[1, x] = x + 1; p[k_, x_] := p[k, x] = x*p[k - 1, x] + (-1)^(n + 1)p[k - 2, x]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]

%K sign,tabl

%O 0,24

%A _Roger L. Bagula_, Oct 06 2006

%E Edited by _N. J. A. Sloane_, Oct 29 2006