Number of ballot sequences of length n having largest ascent 1.

Terms

a(0) =1a(1) =3a(2) =8a(3) =19a(4) =47a(5) =114a(6) =286a(7) =723a(8) =1869a(9) =4870a(10) =12943a(11) =34662a(12) =94055a(13) =257397a(14) =712102a(15) =1983341a(16) =5574561a(17) =15767323a(18) =44933781a(19) =128791036a(20) =371525354a(21) =1077236361a(22) =3141339436a(23) =9203555415a(24) =27098848505a(25) =80132017267a(26) =238015965927a(27) =709753560742