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

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =36a(6) =104a(7) =309a(8) =939a(9) =2905a(10) =9118a(11) =28964a(12) =92940a(13) =300808a(14) =980864a(15) =3219205a(16) =10626023a(17) =35252867a(18) =117485454a(19) =393133485a(20) =1320357501a(21) =4449298136a(22) =15038769672a(23) =50973266380a(24) =173214422068a(25) =589998043276