Symmetries in unrooted (1,3) trees on 2n vertices.

Terms

a(0) =2a(1) =6a(2) =8a(3) =8a(4) =56a(5) =24a(6) =168a(7) =240a(8) =608a(9) =920a(10) =5680a(11) =6104a(12) =18416a(13) =43008a(14) =148152a(15) =325608a(16) =980840a(17) =2421096a(18) =7336488a(19) =19769312a(20) =58192608a(21) =164776248a(22) =502085760a(23) =1427051544a(24) =4261678656a(25) =12615722288a(26) =37914214232a(27) =113567513528a(28) =343641240328