Number of noncrossing partitions of an n-set with distinct block sizes.

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =5a(5) =11a(6) =43a(7) =64a(8) =137a(9) =253a(10) =1121a(11) =1596a(12) =3625a(13) =6475a(14) =12825a(15) =51766a(16) =77393a(17) =163609a(18) =299719a(19) =577126a(20) =980581a(21) =4105291a(22) =5770601a(23) =12332486a(24) =21758449a(25) =41755501a(26) =69558113a(27) =127657648a(28) =466063781a(29) =669034815