Number of Dyck paths of semilength n with a valley (DU) spanning the midpoint.

Terms

a(0) =0a(1) =1a(2) =1a(3) =5a(4) =10a(5) =42a(6) =107a(7) =429a(8) =1234a(9) =4862a(10) =15032a(11) =58786a(12) =190588a(13) =742900a(14) =2490399a(15) =9694845a(16) =33312770a(17) =129644790a(18) =453999656a(19) =1767263190a(20) =6282014804a(21) =24466267020a(22) =88026769844a(23) =343059613650