A123254 Triangle T(n,k), 0<=k<=n, read by rows given by [ -1,1,-1,1,-1,1,-1,1,-1,1,...] DELTA [1,-1,1,-1,1,-1,1,-1,1,-1,...] where DELTA is the operator defined in A084938.

1, -1, 1, 0, 0, 0, 1, -3, 3, -1, 0, 0, 0, 0, 0, -2, 10, -20, 20, -10, 2, 0, 0, 0, 0, 0, 0, 0, 5, -35, 105, -175, 175, -105, 35, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 126, -504, 1176, -1764, 1764, -1176, 504, -126, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Oct 08 2006

Keywords

• sign
• tabl

Examples

			Triangle begins:
1;
-1, 1;
0, 0, 0;
1, -3, 3, -1;
0, 0, 0, 0, 0;
-2, 10, -20, 20, -10, 2;
0, 0, 0, 0, 0, 0, 0;
5, -35, 105, -175, 175, -106, 35, -5;
0, 0, 0, 0, 0, 0, 0, 0, 0;
		

Crossrefs

Cf. A000108, A007318.

Formula

T(n,k)=(-1)^k*A105523(n)*binomial(n,k) . T(n,n)=A090192(n) . Sum_{k, 0<=k<=n}T(n,k)= 0^n= A000007(n).