A155050 A symmetric Catalan based triangle.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 2, 5, 5, 2, 1, 1, 1, 1, 2, 5, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 42, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 42, 42, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 42, 132, 42, 14, 5, 2, 1, 1

Offset: 0

Author

Paul Barry, Jan 19 2009

Keywords

• easy
• nonn
• tabl

Comments

Central coefficients are A000108. Row sums are A155051.

Image under Riordan array ((1+x)/(1-x),x)^{-1} is A155052.

Examples

			Triangle begins
1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 1, 2, 1, 1,
1, 1, 2, 2, 1, 1,
1, 1, 2, 5, 2, 1, 1,
1, 1, 2, 5, 5, 2, 1, 1,
1, 1, 2, 5, 14, 5, 2, 1, 1,
1, 1, 2, 5, 14, 14, 5, 2, 1, 1,
1, 1, 2, 5, 14, 42, 14, 5, 2, 1, 1
		

Crossrefs

Cf. A000108, A155051

Formula

Number triangle T(n,k)=sum{j=0..n, [j<=k]*[j<=n-k]*(ct(j+1)-ct(j))} where ct(n):=if(n=0,0,A000108(n-1)).

T(n,k) = A000108(min(k, n-k)). - Philippe Deléham, Feb 26 2014