Number of prime binary rooted trees with n external nodes.

Terms

a(0) =1a(1) =2a(2) =4a(3) =14a(4) =38a(5) =132a(6) =420a(7) =1426a(8) =4834a(9) =16796a(10) =58688a(11) =208012a(12) =742636a(13) =2674384a(14) =9693976a(15) =35357670a(16) =129641774a(17) =477638700a(18) =1767253368a(19) =6564119892a(20) =24466233428a(21) =91482563640a(22) =343059494120