a(n) = T(2n,n), array T as in A038738.

Terms

a(0) =1a(1) =5a(2) =30a(3) =188a(4) =1201a(5) =7756a(6) =50439a(7) =329625a(8) =2161974a(9) =14220038a(10) =93740152a(11) =619083041a(12) =4094863900a(13) =27120465023a(14) =179822255181