Number of rooted trees of 2n+1 nodes with every leaf at height n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =9a(6) =17a(7) =28a(8) =49a(9) =83a(10) =145a(11) =246a(12) =427a(13) =729a(14) =1256a(15) =2152a(16) =3702a(17) =6341a(18) =10892a(19) =18662a(20) =32016a(21) =54853a(22) =94034a(23) =161055a(24) =275929a(25) =472461a(26) =809033a(27) =1384848a(28) =2370434a(29) =4056309