Number of ordered rooted trees with n non-root nodes and all outdegrees <= four.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =41a(6) =125a(7) =393a(8) =1265a(9) =4147a(10) =13798a(11) =46476a(12) =158170a(13) =543050a(14) =1878670a(15) =6542330a(16) =22915999a(17) =80682987a(18) =285378270a(19) =1013564805a(20) =3613262795a(21) =12924536005a(22) =46373266470a(23) =166856922125a(24) =601928551824