Number of Dyck paths of semilength n with no DDUU.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =35a(6) =97a(7) =275a(8) =794a(9) =2327a(10) =6905a(11) =20705a(12) =62642a(13) =190987a(14) =586219a(15) =1810011a(16) =5617914a(17) =17518463a(18) =54857506a(19) =172431935a(20) =543861219a(21) =1720737981a(22) =5459867166a(23) =17369553427a(24) =55391735455a(25) =177040109419a(26) =567019562429