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

Terms

a(0) =4a(1) =8a(2) =48a(3) =400a(4) =3920a(5) =42336a(6) =487872a(7) =5889312a(8) =73616400a(9) =945561760a(10) =12412647104a(11) =165878102208