A117362 Riordan array (1-2x,x(1-x)).

1, -2, 1, 0, -3, 1, 0, 2, -4, 1, 0, 0, 5, -5, 1, 0, 0, -2, 9, -6, 1, 0, 0, 0, -7, 14, -7, 1, 0, 0, 0, 2, -16, 20, -8, 1, 0, 0, 0, 0, 9, -30, 27, -9, 1, 0, 0, 0, 0, -2, 25, -50, 35, -10, 1, 0, 0, 0, 0, 0, -11, 55, -77, 44, -11, 1

Offset: 0

Author

Paul Barry, Mar 10 2006

Keywords

• easy
• sign
• tabl

Comments

A signed version of A113214. Inverse of A092392. Row sums are A100051(n+1) with g.f. (1-2x)/(1-x+x^2). Diagonal sums are A117363.

Examples

			Triangle begins
1,
-2, 1,
0, -3, 1,
0, 2, -4, 1,
0, 0, 5, -5, 1,
0, 0, -2, 9, -6, 1,
0, 0, 0, -7, 14, -7, 1,
0, 0, 0, 2, -16, 20, -8, 1
		

Formula

Number triangle T(n,k)=(-1)^(n-k)(C(k,n-k)+2*C(k, n-k-1))