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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =11a(7) =22a(8) =43a(9) =90a(10) =185a(11) =393a(12) =835a(13) =1802a(14) =3904a(15) =8540a(16) =18756a(17) =41463a(18) =92022a(19) =205179a(20) =459086a(21) =1030917a(22) =2321949a(23) =5245104a(24) =11878750a(25) =26967957a(26) =61359917a(27) =139902251a(28) =319591669a(29) =731385621