Diagonal sums of correlation triangle for Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =19a(5) =52a(6) =162a(7) =505a(8) =1666a(9) =5576a(10) =19135a(11) =66494a(12) =234316a(13) =833620a(14) =2992817a(15) =10822802a(16) =39395434a(17) =144207387a(18) =530534468a(19) =1960521470a(20) =7273963575a(21) =27085625086a(22) =101188629692a(23) =379160330195