a(n) = C(n)*(5*n+1) where C(n) = Catalan numbers (A000108).

Terms

a(0) =1a(1) =6a(2) =22a(3) =80a(4) =294a(5) =1092a(6) =4092a(7) =15444a(8) =58630a(9) =223652a(10) =856596a(11) =3292016a(12) =12688732a(13) =49031400a(14) =189885240a(15) =736808220a(16) =2863971270a(17) =11149451940a(18) =43465121700a(19) =169657266240a(20) =662976162420