Number of Dyck paths of semilength n with no peak at height 4.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =35a(6) =97a(7) =276a(8) =805a(9) =2404a(10) =7343a(11) =22916a(12) =72980a(13) =236857a(14) =782275a(15) =2625265a(16) =8938718a(17) =30834165a(18) =107608097a(19) =379454447a(20) =1350434278a(21) =4845475311a(22) =17512579630a(23) =63703732426a(24) =233063976059a(25) =857067469749