Number of rooted trees on n nodes with thinning limbs.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =21a(7) =38a(8) =78a(9) =153a(10) =314a(11) =632a(12) =1313a(13) =2700a(14) =5646a(15) =11786a(16) =24831a(17) =52348a(18) =111027a(19) =235834a(20) =502986a(21) =1074739a(22) =2303146a(23) =4944507a(24) =10639201a(25) =22930493a(26) =49511948a(27) =107065966a(28) =231874164a(29) =502834328