A124394 Inverse of Fine number renewal array.

1, 0, 1, -1, 0, 1, -2, -2, 0, 1, -3, -4, -3, 0, 1, -4, -5, -6, -4, 0, 1, -5, -4, -6, -8, -5, 0, 1, -6, 0, 0, -6, -10, -6, 0, 1, -7, 8, 14, 8, -5, -12, -7, 0, 1, -8, 21, 36, 36, 20, -3, -14, -8, 0, 1, -9, 40, 63, 72, 65, 36, 0, -16, -9, 0, 1

Offset: 0

Author

Paul Barry, Oct 30 2006

Keywords

• easy
• sign
• tabl

Comments

Inverse of A065600. Row sums are A057681(n+1). Diagonal sums are A124395.

Examples

			Triangle begins
1,
0, 1,
-1, 0, 1,
-2, -2, 0, 1,
-3, -4, -3, 0, 1,
-4, -5, -6, -4, 0, 1,
-5, -4, -6, -8, -5, 0, 1,
-6, 0, 0, -6, -10, -6, 0, 1
		

Formula

Riordan array ((1-2x)/(1-x)^2,x(1-2x)/(1-x)^2); Number triangle T(n,k)=sum{j=0..k+1, C(k+1,j)C(n-j+k+1,2k+1)(-2)^j};