Number of symmetric Dyck paths of semilength n and having no hills (i.e., no peaks at level 1).

Terms

a(0) =1a(1) =0a(2) =1a(3) =2a(4) =4a(5) =6a(6) =13a(7) =22a(8) =46a(9) =80a(10) =166a(11) =296a(12) =610a(13) =1106a(14) =2269a(15) =4166a(16) =8518a(17) =15792a(18) =32206a(19) =60172a(20) =122464a(21) =230252a(22) =467842a(23) =884236a(24) =1794196a(25) =3406104a(26) =6903352a(27) =13154948a(28) =26635774a(29) =50922986