Number of Dyck paths of semilength n with distinct peak heights.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =13a(6) =31a(7) =71a(8) =181a(9) =447a(10) =1111a(11) =2799a(12) =7083a(13) =17939a(14) =45563a(15) =115997a(16) =295827a(17) =755275a(18) =1929917a(19) =4935701a(20) =12631111a(21) =32340473a(22) =82837041a(23) =212248769a(24) =543978897a(25) =1394481417a(26) =3575356033a(27) =9168277483a(28) =23512924909a(29) =60306860253