Number of maximal antichains in rooted plane trees on n nodes.

Terms

a(0) =1a(1) =2a(2) =5a(3) =15a(4) =50a(5) =178a(6) =663a(7) =2553a(8) =10086a(9) =40669a(10) =166752a(11) =693331a(12) =2917088a(13) =12398545a(14) =53164201a(15) =229729439a(16) =999460624a(17) =4374546305a(18) =19250233408a(19) =85120272755a(20) =378021050306