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

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =6a(5) =26a(6) =97a(7) =333a(8) =1085a(9) =3411a(10) =10448a(11) =31376a(12) =92773a(13) =270907a(14) =783003a(15) =2243815a(16) =6383550a(17) =18048494a(18) =50755897a(19) =142067625a(20) =396014681a(21) =1099863867a(22) =3044737100a(23) =8404071596a(24) =23135752141a(25) =63538808311a(26) =174120317367a(27) =476207551183