a(n) = 2*3^n*(2*n)!/(n!*(n+2)!).

Terms

a(0) =1a(1) =2a(2) =9a(3) =54a(4) =378a(5) =2916a(6) =24057a(7) =208494a(8) =1876446a(9) =17399772a(10) =165297834a(11) =1602117468a(12) =15792300756a(13) =157923007560