A188316 Riordan array (1/(1-x^2), x/((1-x)*(1-x^2))).

1, 0, 1, 1, 1, 1, 0, 3, 2, 1, 1, 3, 6, 3, 1, 0, 6, 10, 10, 4, 1, 1, 6, 20, 22, 15, 5, 1, 0, 10, 30, 49, 40, 21, 6, 1, 1, 10, 50, 91, 100, 65, 28, 7, 1, 0, 15, 70, 168, 216, 181, 98, 36, 8, 1, 1, 15, 105, 280, 444, 441, 301, 140, 45, 9, 1

Offset: 0

Author

Paul Barry, Mar 28 2011

Keywords

• nonn
• tabl

Comments

Row sums are A077998.

Diagonal sums are A052547.

Inverse is A188317.

Examples

			Triangle begins
1,
0, 1,
1, 1, 1,
0, 3, 2, 1,
1, 3, 6, 3, 1,
0, 6, 10, 10, 4, 1,
1, 6, 20, 22, 15, 5, 1,
0, 10, 30, 49, 40, 21, 6, 1,
1, 10, 50, 91, 100, 65, 28, 7, 1,
0, 15, 70, 168, 216, 181, 98, 36, 8, 1
		

Formula

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) - T(n-3,k), T(0,0) = T(1,1) = T(2,0) = T(2,1) = T(2,2)=1, T(1,0)=0, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 16 2014