Number of rooted trees with n nodes having some subtrees replaced by cycles.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =2a(5) =4a(6) =9a(7) =23a(8) =61a(9) =168a(10) =469a(11) =1326a(12) =3776a(13) =10833a(14) =31228a(15) =90438a(16) =262860a(17) =766497a(18) =2241194a(19) =6569206a(20) =19296214a(21) =56789286a(22) =167419568a(23) =494337282a(24) =1461690270a(25) =4327638394a(26) =12828158828a(27) =38067670764a(28) =113081627856a(29) =336233591365