A124341 Riordan array (1/(1+x), x(1+2x)/(1+x)^2).

1, -1, 1, 1, -1, 1, -1, 0, -1, 1, 1, 2, -1, -1, 1, -1, -5, 5, -2, -1, 1, 1, 9, -10, 8, -3, -1, 1, -1, -14, 14, -14, 11, -4, -1, 1, 1, 20, -14, 14, -17, 14, -5, -1, 1, -1, -27, 6, 0, 9, -19, 17, -6, -1, 1, 1, 35

Offset: 0

Author

Paul Barry, Oct 26 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are (-1)^n*F(n-1), the inverse binomial transform of F(n+1). Diagonal sums are A124342.

Examples

			Triangle begins
1;
-1, 1;
1, -1, 1;
-1, 0, -1, 1;
1, 2, -1, -1, 1;
-1, -5, 5, -2, -1, 1;
1, 9, -10, 8, -3, -1, 1;
-1, -14, 14, -14, 11, -4, -1, 1;
1, 20, -14, 14, -17, 14, -5, -1, 1;
		

Formula

Number triangle T(n,k)=sum{j=0..n, (-1)^(n-j)*C(n,j)*C(k,j-k)}; T(n,k)=sum{j=0..n, (-1)^(j-k)*C(k,n-j)*C(n,j-k)}.

T(n,k)=T(n-1,k-1)-2*T(n-1,k)+2*T(n-2,k-1)-T(n-2,k), T(0,0)=1, T(1,0)=-1, T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 12 2014

Extensions

More terms from Philippe Deléham, Dec 19 2011