Number of decorated Dyck paths of length n ending at arbitrary levels.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =11a(6) =26a(7) =43a(8) =102a(9) =175a(10) =416a(11) =733a(12) =1745a(13) =3137a(14) =7476a(15) =13651a(16) =32559a(17) =60199a(18) =143672a(19) =268369a(20) =640823a(21) =1207277a(22) =2884008a(23) =5472821a(24) =13078414a(25) =24973213a(26) =59696622a(27) =114609547a(28) =274037261a(29) =528622499