a(n) = C(floor(n/2 + 1/2))*C(floor(n/2 + 1)) where C(i) = Catalan numbers A000108.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =25a(6) =70a(7) =196a(8) =588a(9) =1764a(10) =5544a(11) =17424a(12) =56628a(13) =184041a(14) =613470a(15) =2044900a(16) =6952660a(17) =23639044a(18) =81662152a(19) =282105616a(20) =987369656a(21) =3455793796a(22) =12228193432a(23) =43268992144a(24) =154532114800a(25) =551900410000