Number of rooted trees with n nodes and 2-colored non-leaf nodes.

Terms

a(0) =1a(1) =2a(2) =6a(3) =18a(4) =60a(5) =204a(6) =734a(7) =2694a(8) =10162a(9) =38982a(10) =151920a(11) =599244a(12) =2389028a(13) =9608668a(14) =38945230a(15) =158904230a(16) =652178206a(17) =2690598570a(18) =11151718166a(19) =46412717826a(20) =193891596436a(21) =812748036380