Number of trees with n vertices rooted at a non-edge.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =9a(5) =27a(6) =79a(7) =233a(8) =679a(9) =1987a(10) =5784a(11) =16864a(12) =49063a(13) =142821a(14) =415439a(15) =1208761a(16) =3516475a(17) =10232428a(18) =29778138a(19) =86682119a(20) =252382445a(21) =735040515a(22) =2141319946a(23) =6239913801a(24) =18188637903a(25) =53033228465a(26) =154674931182a(27) =451247206423