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

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =5a(5) =10a(6) =24a(7) =57a(8) =144a(9) =360a(10) =923a(11) =2382a(12) =6246a(13) =16486a(14) =43917a(15) =117692a(16) =317447a(17) =860574a(18) =2344396a(19) =6413119a(20) =17611086a(21) =48527597a(22) =134141819a(23) =371862485a(24) =1033588413a(25) =2879818379a(26) =8041870070a(27) =22503533295a(28) =63093284667a(29) =177213424466