Number of subwords of the form DUUD or DDUUD in nondecreasing Dyck paths of length 2n.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =5a(5) =18a(6) =59a(7) =185a(8) =564a(9) =1685a(10) =4957a(11) =14406a(12) =41455a(13) =118321a(14) =335400a(15) =945193a(16) =2650229a(17) =7398330a(18) =20573219a(19) =57013865a(20) =157517532a(21) =433993661a(22) =1192779085a(23) =3270835566a(24) =8950887895a(25) =24448816993a(26) =66665369424a(27) =181489721425a(28) =493361278949