A124237 Riordan array (1/(1-2x), x/((1-x)(1-2x))).

1, 2, 1, 4, 5, 1, 8, 17, 8, 1, 16, 49, 39, 11, 1, 32, 129, 150, 70, 14, 1, 64, 321, 501, 338, 110, 17, 1, 128, 769, 1524, 1375, 640, 159, 20, 1, 256, 1793, 4339, 4973, 3075, 1083, 217, 23, 1, 512, 4097, 11762, 16508

Offset: 0

Author

Paul Barry, Oct 22 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A007052. Diagonal sums are F(2n+1)=A001519(n+1)=A122367(n). Product of A007318 and Delannoy triangle A008288.

Examples

			Triangle begins
1,
2, 1,
4, 5, 1,
8, 17, 8, 1,
16, 49, 39, 11, 1,
32, 129, 150, 70, 14, 1
		

Formula

Number triangle T(n,k)=sum{j=0..n-k, C(n-j,k)C(n+k,j)}

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 17 2014