Number of ordered trees with n edges and having no root-to-leaf branches.

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =4a(5) =13a(6) =42a(7) =139a(8) =470a(9) =1616a(10) =5632a(11) =19852a(12) =70654a(13) =253559a(14) =916558a(15) =3334211a(16) =12197142a(17) =44842184a(18) =165597008a(19) =613991206a(20) =2284809072a(21) =8530458154a(22) =31945128628a(23) =119960276246a(24) =451621453764