Number of first/rest balanced rooted plane trees with n nodes.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =1a(6) =1a(7) =3a(8) =2a(9) =6a(10) =8a(11) =11a(12) =26a(13) =28a(14) =67a(15) =96a(16) =162a(17) =316a(18) =448a(19) =922a(20) =1435a(21) =2572a(22) =4660a(23) =7563a(24) =14397a(25) =23896a(26) =43337a(27) =77097a(28) =133071a(29) =244787