Number of antichains in rooted plane trees on n nodes.

Terms

a(0) =1a(1) =2a(2) =7a(3) =29a(4) =131a(5) =625a(6) =3099a(7) =15818a(8) =82595a(9) =439259a(10) =2371632a(11) =12967707a(12) =71669167a(13) =399751019a(14) =2247488837a(15) =12723799989a(16) =72474333715a(17) =415046380767