Invariants for a hidden action of S_(n+1) on Cayley trees with n vertices.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =4a(7) =6a(8) =11a(9) =18a(10) =39a(11) =70a(12) =153a(13) =321a(14) =721a(15) =1612a(16) =3792a(17) =8896a(18) =21498a(19) =52230a(20) =128994a(21) =320786a(22) =806582a(23) =2040912a(24) =5205311a(25) =13352470a(26) =34460430a(27) =89384609