Number of Dyck paths of semilength n having no DDUU's starting at level 2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =36a(6) =106a(7) =327a(8) =1045a(9) =3433a(10) =11529a(11) =39414a(12) =136733a(13) =480180a(14) =1703807a(15) =6099193a(16) =22000823a(17) =79890801a(18) =291808480a(19) =1071403389a(20) =3952020216a(21) =14638293671a(22) =54424065467a(23) =203034222400a(24) =759790586108