A115254 Diagonal sums of correlation triangle for Catalan numbers.

1, 1, 3, 7, 19, 52, 162, 505, 1666, 5576, 19135, 66494, 234316, 833620, 2992817, 10822802, 39395434, 144207387, 530534468, 1960521470, 7273963575, 27085625086, 101188629692, 379160330195, 1424634014730, 5366319233160

Offset: 0

Author

Paul Barry, Jan 18 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A115253.

Convolution of A161006 and A079978. - R. J. Mathar, Oct 04 2014

Formula

G.f.: c(x)c(x^2)/(1-x^3) where c(x) is the g.f. of A000108; a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, [j<=k]*C(k-j)[j<=n-2k]*C(n-2k-j)}}.