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

0,13

Comments

Central coefficients are A000108. Row sums are A155051.

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

Links

Table of n, a(n) for n=0..90.

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

Example

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

Sequence in context: A139040 A139147 A055801 * A140356 A119963 A057790

Adjacent sequences: A155047 A155048 A155049 * A155051 A155052 A155053

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 19 2009

Status

approved