Number of DUU's in all length n left factors of Dyck paths; here U=(1,1) and D=(1,-1).

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =3a(6) =9a(7) =21a(8) =52a(9) =113a(10) =261a(11) =550a(12) =1226a(13) =2542a(14) =5546a(15) =11389a(16) =24494a(17) =49989a(18) =106413a(19) =216258a(20) =456826a(21) =925586a(22) =1943550a(23) =3929090a(24) =8210896a(25) =16571018a(26) =34494114a(27) =69523116a(28) =144246532a(29) =290424604