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

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =7a(6) =30a(7) =109a(8) =365a(9) =1164a(10) =3593a(11) =10835a(12) =32106a(13) =93845a(14) =271321a(15) =777432a(16) =2211025a(17) =6248479a(18) =17562870a(19) =49132669a(20) =136884293a(21) =379975140a(22) =1051356761a(23) =2900587115a(24) =7981564866a(25) =21911096357a(26) =60021530545a(27) =164095925424a(28) =447823729825