Number of unlabeled rooted 2,3 cacti (triangular cacti with bridges).

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =21a(5) =60a(6) =190a(7) =600a(8) =1977a(9) =6589a(10) =22408a(11) =77050a(12) =268178a(13) =941599a(14) =3333585a(15) =11882427a(16) =42615480a(17) =153653039a(18) =556664752a(19) =2025330509a(20) =7397242875a(21) =27111563026a(22) =99681629658a(23) =367563272278