a(n) = C(n)*(4*n+1) where C(n) = Catalan numbers (A000108).

Terms

a(0) =1a(1) =5a(2) =18a(3) =65a(4) =238a(5) =882a(6) =3300a(7) =12441a(8) =47190a(9) =179894a(10) =688636a(11) =2645370a(12) =10192588a(13) =39373700a(14) =152443080a(15) =591385545a(16) =2298248550a(17) =8945490510a(18) =34867625100a(19) =136079265630a(20) =531693754020