Number of decorated Dyck paths of length n without peaks at level 1 ending at arbitrary levels.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =8a(6) =18a(7) =31a(8) =71a(9) =126a(10) =290a(11) =527a(12) =1218a(13) =2253a(14) =5223a(15) =9796a(16) =22763a(17) =43170a(18) =100502a(19) =192347a(20) =448476a(21) =864887a(22) =2019121a(23) =3919162a(24) =9159252a(25) =17877619a(26) =41819003a(27) =82021628a(28) =192015633