A111526 Number triangle T(n,k)=C((n+k)/2,k)(n+1)(1+(-1)^(n-k))/(2(k+1)); T(n,k)=(-1)^((n-k)/2)*A053120(n+1,k+1)/2^k; 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, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1, 13, 0, 91, 0, 182, 0, 156, 0, 65, 0, 13, 0, 1, 0

Offset: 0

Author

Paul Barry, Aug 05 2005

Keywords

• easy
• nonn
• tabl

Comments

A scaled Chebyshev triangle.

Row sums are A001350(n+1). Diagonal sums are A033484, with interpolated zeros. Inverse is A111527.

Examples

			Triangle starts
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;
		

Crossrefs

Cf. A110813.