Number of Dyck paths containing exactly one UUUD.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =5a(5) =21a(6) =78a(7) =274a(8) =927a(9) =3061a(10) =9933a(11) =31824a(12) =100972a(13) =317942a(14) =995088a(15) =3099105a(16) =9612735a(17) =29715525a(18) =91595391a(19) =281643480a(20) =864189486a(21) =2646805668a(22) =8093543439a(23) =24713953515a(24) =75370741506a(25) =229604257846a(26) =698754428388