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

Terms

a(0) =1a(1) =2a(2) =2a(3) =10a(4) =14a(5) =42a(6) =90a(7) =354a(8) =758a(9) =2290a(10) =6002a(11) =18410a(12) =51310a(13) =154106a(14) =449322a(15) =1384962a(16) =4089174a(17) =12475362a(18) =37746786a(19) =116037642a(20) =355367310a(21) =1097869386a(22) =3393063162a(23) =10546081122a(24) =32810171382a(25) =102465452754a(26) =320522209490