Number of Dyck n-paths all of whose ascents and descents have prime lengths.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =1a(5) =4a(6) =2a(7) =10a(8) =10a(9) =22a(10) =46a(11) =64a(12) =167a(13) =245a(14) =560a(15) =1035a(16) =1978a(17) =4210a(18) =7715a(19) =16497a(20) =31929a(21) =65216a(22) =133295a(23) =266244a(24) =553750a(25) =1116404a(26) =2308931a(27) =4738660a(28) =9742795a(29) =20204902