Number of subwords of the form UUUD in nondecreasing Dyck paths of length 2n.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =5a(5) =18a(6) =60a(7) =191a(8) =589a(9) =1775a(10) =5257a(11) =15360a(12) =44394a(13) =127171a(14) =361595a(15) =1021693a(16) =2871245a(17) =8031246a(18) =22372344a(19) =62096135a(20) =171797257a(21) =473928875a(22) =1304007889a(23) =3579517116a(24) =9804791910a(25) =26804181643a(26) =73145473655a(27) =199276078201a(28) =542076556949