Number of trees with n nodes and 2-colored internal (non-leaf) nodes.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =12a(6) =33a(7) =98a(8) =305a(9) =1002a(10) =3424a(11) =12016a(12) =43230a(13) =158516a(14) =590621a(15) =2230450a(16) =8521967a(17) =32889238a(18) =128064009a(19) =502590642a(20) =1986357307a(21) =7900377892a(22) =31602819524a(23) =127076645038a(24) =513419837168