Number of ballot sequences of length n having 3 largest parts.

Terms

a(0) =1a(1) =0a(2) =0a(3) =5a(4) =14a(5) =28a(6) =90a(7) =285a(8) =1232a(9) =4378a(10) =17082a(11) =65338a(12) =269775a(13) =1148080a(14) =5111730a(15) =23047359a(16) =107594036a(17) =507358368a(18) =2479868846a(19) =12286215326a(20) =62819732813a(21) =325860325750