Number of Dyck paths of semilength n such that no positive level has fewer than four peaks.

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =1a(6) =1a(7) =1a(8) =1a(9) =6a(10) =57a(11) =247a(12) =718a(13) =1795a(14) =4210a(15) =9969a(16) =27596a(17) =98507a(18) =402924a(19) =1626525a(20) =6142611a(21) =21729644a(22) =73308577a(23) =241270869a(24) =793679894a(25) =2666563900a(26) =9263663359a(27) =33259282181a(28) =122178034000a(29) =453573262015