a(n) = Catalan(n)^2*(4n + 2).

Terms

a(0) =2a(1) =6a(2) =40a(3) =350a(4) =3528a(5) =38808a(6) =453024a(7) =5521230a(8) =69526600a(9) =898283672a(10) =11848435872a(11) =158966514616