a(n) = number of unlabeled rooted trees on n nodes with an odd number of endpoints.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =10a(6) =24a(7) =58a(8) =142a(9) =359a(10) =919a(11) =2384a(12) =6240a(13) =16487a(14) =43894a(15) =117689a(16) =317400a(17) =860585a(18) =2344280a(19) =6413109a(20) =17610746a(21) =48527584a(22) =134141036a(23) =371862499a(24) =1033586232a(25) =2879818131a(26) =8041864259a(27) =22503532974a(28) =63093269641a(29) =177213423131