Number of ballot sequences of length n having largest descent 2.

Terms

a(0) =1a(1) =5a(2) =21a(3) =78a(4) =292a(5) =1028a(6) =3691a(7) =13004a(8) =46452a(9) =165098a(10) =595386a(11) =2148830a(12) =7861261a(13) =28880866a(14) =107407411a(15) =401862116a(16) =1520528499a(17) =5791624015a(18) =22288596981a(19) =86362655462a(20) =337798945830