Number of Dyck paths of semilength n having no UDDU's starting at level 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =29a(6) =90a(7) =290a(8) =960a(9) =3246a(10) =11164a(11) =38934a(12) =137358a(13) =489341a(14) =1757882a(15) =6360634a(16) =23160528a(17) =84802606a(18) =312041692a(19) =1153271984a(20) =4279311348a(21) =15935808866a(22) =59537435012a(23) =223099337404a(24) =838282693560