Number of binary rooted trees with n nodes and internal path length n.

Terms

a(0) =1a(1) =1a(2) =0a(3) =2a(4) =0a(5) =1a(6) =4a(7) =0a(8) =4a(9) =2a(10) =8a(11) =6a(12) =8a(13) =8a(14) =8a(15) =40a(16) =4a(17) =29a(18) =40a(19) =52a(20) =56a(21) =64a(22) =116a(23) =112a(24) =200a(25) =86a(26) =296a(27) =366a(28) =360a(29) =432