A158020 Triangle of coefficients in expansion of (-1-x)^floor(n/2)(1-x)^ceiling(n/2).

1, 1, -1, -1, 0, 1, -1, 1, 1, -1, 1, 0, -2, 0, 1, 1, -1, -2, 2, 1, -1, -1, 0, 3, 0, -3, 0, 1, -1, 1, 3, -3, -3, 3, 1, -1, 1, 0, -4, 0, 6, 0, -4, 0, 1, 1, -1, -4, 4, 6, -6, -4, 4, 1, -1, -1, 0, 5, 0, -10, 0, 10, 0, -5, 0, 1, -1, 1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1

Offset: 0

Author

Philippe Deléham, Mar 11 2009

Keywords

• sign
• tabl

Comments

Triangle T(n,k), 0 <= k <= n, read by rows given by [1,-2,1,0,0,0,0,0,0,...] DELTA [-1,0,1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

Examples

			Triangle begins:
   1;
   1, -1;
  -1,  0,  1;
  -1,  1,  1, -1;
   1,  0, -2,  0,  1;  ...
		

Crossrefs

Cf. A051160.

Programs

Mathematica

Flatten[Table[CoefficientList[(-1 - x)^Floor[n/2] (1 - x)^Ceiling[n/2], x], {n, 0, 11}]] (* T. D. Noe, Dec 01 2011 *)

Formula

T(n,k) = T(n-2,k-2) - T(n-2,k), T(0,0)=T(1,0)=1, T(1,1)=-1.

G.f.: (1+(1-y)*x)/(1+(1-y^2)*x^2). - Philippe Deléham, Dec 02 2011

Extensions

Corrected by Philippe Deléham, Dec 02 2011