Number of Dyck paths of semilength n with no UUDU's starting at level 0.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =28a(6) =85a(7) =271a(8) =893a(9) =3013a(10) =10351a(11) =36075a(12) =127219a(13) =453097a(14) =1627378a(15) =5887660a(16) =21436354a(17) =78484402a(18) =288779728a(19) =1067263660a(20) =3960081904a(21) =14746806292a(22) =55094725918a(23) =206450572930a(24) =775724723086