A113955 Riordan array (1/((1-4x)c(x)),xc(x)/sqrt(1-4x)), c(x) the g.f. of A000108.

1, 3, 1, 11, 6, 1, 42, 30, 9, 1, 163, 140, 58, 12, 1, 638, 630, 325, 95, 15, 1, 2510, 2772, 1686, 624, 141, 18, 1, 9908, 12012, 8330, 3682, 1064, 196, 21, 1, 39203, 51480, 39796, 20264, 7050, 1672, 260, 24, 1, 155382, 218790, 185517, 106203, 42849, 12303, 2475

Offset: 0

Author

Paul Barry, Nov 09 2005

Keywords

• easy
• nonn
• tabl

Comments

Columns include A032443,A002457,A018218,A038836. Row sums are A100192. Diagonal sums are A113956.

Examples

			Triangle begins
1;
3, 1;
11, 6, 1;
42, 30, 9, 1;
163, 140, 58, 12, 1;
638, 630, 325, 95, 15, 1;
		

Formula

Riordan array ((1/(1-4x)+1/sqrt(1-4x))/2, (2x/((1-4x)+sqrt(1-4x)))); Number triangle T(n, k)=sum{j=0..n, C(j, j-k)C(2n, n-j)}.

T(n,k)=sum{j=0..n, C(2n,j)C(n-j,k)}; - Paul Barry, Apr 03 2006