Number of ballot sequences of length n having 6 largest parts.

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =132a(7) =429a(8) =1001a(9) =2002a(10) =3640a(11) =6188a(12) =97512a(13) =569772a(14) =3625998a(15) =14847987a(16) =62772941a(17) =211719508a(18) =877100400a(19) =3621910050a(20) =21265454080a(21) =120016339560a(22) =727205489010