Number of ballot sequences of length n having exactly 1 largest part.

Terms

a(0) =0a(1) =1a(2) =1a(3) =3a(4) =7a(5) =20a(6) =56a(7) =182a(8) =589a(9) =2088a(10) =7522a(11) =28820a(12) =113092a(13) =464477a(14) =1955760a(15) =8541860a(16) =38215077a(17) =176316928a(18) =832181774a(19) =4033814912a(20) =19973824386a(21) =101257416701a(22) =523648869394