a(n) = 2*Catalan(n) - Catalan(n-1).

Terms

a(0) =1a(1) =3a(2) =8a(3) =23a(4) =70a(5) =222a(6) =726a(7) =2431a(8) =8294a(9) =28730a(10) =100776a(11) =357238a(12) =1277788a(13) =4605980a(14) =16715250a(15) =61020495a(16) =223931910a(17) =825632610a(18) =3056887680a(19) =11360977650a(20) =42368413620a(21) =158498860260a(22) =594636663660