Number of Dyck paths of semilength n such that no level has more than two peaks.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =12a(5) =31a(6) =90a(7) =264a(8) =797a(9) =2402a(10) =7355a(11) =22725a(12) =70573a(13) =220007a(14) =688379a(15) =2160568a(16) =6798020a(17) =21428295a(18) =67644503a(19) =213806475a(20) =676499166a(21) =2142338437a(22) =6789119425a(23) =21527297986a(24) =68292751071a(25) =216737768906a(26) =688082702872