%I #4 Oct 04 2014 11:42:59
%S 1,1,3,7,19,52,162,505,1666,5576,19135,66494,234316,833620,2992817,
%T 10822802,39395434,144207387,530534468,1960521470,7273963575,
%U 27085625086,101188629692,379160330195,1424634014730,5366319233160
%N Diagonal sums of correlation triangle for Catalan numbers.
%C Diagonal sums of number triangle A115253.
%C Convolution of A161006 and A079978. - _R. J. Mathar_, Oct 04 2014
%F 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)}}.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jan 18 2006