Number of Dyck paths of semilength n with no peak at height 3.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =22a(6) =58a(7) =163a(8) =483a(9) =1494a(10) =4783a(11) =15740a(12) =52956a(13) =181391a(14) =630533a(15) =2218761a(16) =7888266a(17) =28291588a(18) =102237141a(19) =371884771a(20) =1360527143a(21) =5002837936a(22) =18479695171a(23) =68539149518a(24) =255137783916a(25) =952914971191