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

Terms

a(0) =0a(1) =0a(2) =1a(3) =4a(4) =14a(5) =45a(6) =138a(7) =411a(8) =1200a(9) =3454a(10) =9836a(11) =27779a(12) =77938a(13) =217493a(14) =604222a(15) =1672246a(16) =4613030a(17) =12689265a(18) =34817418a(19) =95320335a(20) =260436588a(21) =710278318a(22) =1933906496a(23) =5257545599a(24) =14273273314a(25) =38699274665a(26) =104799960058a(27) =283487736166a(28) =766045036730