Number of semi-lone-child-avoiding rooted trees with n unlabeled vertices.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =7a(6) =15a(7) =29a(8) =62a(9) =129a(10) =279a(11) =602a(12) =1326a(13) =2928a(14) =6544a(15) =14692a(16) =33233a(17) =75512a(18) =172506a(19) =395633a(20) =911108a(21) =2105261a(22) =4880535a(23) =11346694a(24) =26451357a(25) =61813588a(26) =144781303a(27) =339820852a(28) =799168292a(29) =1882845298