Number of labeled trees of diameter 3 with n nodes.

Terms

a(0) =12a(1) =60a(2) =210a(3) =630a(4) =1736a(5) =4536a(6) =11430a(7) =28050a(8) =67452a(9) =159588a(10) =372554a(11) =859950a(12) =1965840a(13) =4456176a(14) =10026702a(15) =22412970a(16) =49806980a(17) =110100060a(18) =242220594a(19) =530578950a(20) =1157627352a(21) =2516581800a(22) =5452594550a(23) =11777604930a(24) =25367149836a(25) =54492396756a(26) =116769422490a(27) =249644973150