A117179 Riordan array ((1-x^2)/(1+x^2)^2,x/(1+x^2)).

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

Offset: 0

Author

Paul Barry, Mar 01 2006

Keywords

• easy
• sign
• tabl

Comments

Inverse is A117178. Row sums are (-1)^n*A098554(n+1). Diagonal sums are 1,0,-2,0,2,0,-2,... with g.f. (1-x^2)/(1+x^2).

Apparently, with the rows de-aerated and then reversed, this matrix becomes signed A034807 with the twos on the diagonal removed. Apparently, |D(2n,k+1)| = |D(2(n-1),k+1)| + |D(2n,k)| where D(n,k) is the k-th element on the n-th diagonal. - Tom Copeland, May 30 2017

Examples

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