Number of n-node rooted trees of height equal to the number of internal (non-leaf) nodes.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =4a(6) =14a(7) =41a(8) =111a(9) =282a(10) =688a(11) =1627a(12) =3761a(13) =8540a(14) =19122a(15) =42333a(16) =92851a(17) =202078a(18) =436916a(19) =939359a(20) =2009781a(21) =4281696a(22) =9087670a(23) =19223905a(24) =40544951a(25) =85284194a(26) =178956984a(27) =374691171a(28) =782936761a(29) =1632982372