Number of Dyck paths of semilength n with no DUUU's starting at level 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =36a(6) =105a(7) =320a(8) =1011a(9) =3289a(10) =10957a(11) =37216a(12) =128435a(13) =449142a(14) =1588228a(15) =5669505a(16) =20403322a(17) =73945553a(18) =269647630a(19) =988642372a(20) =3642310793a(21) =13476857235a(22) =50059454347a(23) =186598634398a(24) =697777187275