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

Terms

a(0) =1a(1) =4a(2) =13a(3) =37a(4) =100a(5) =265a(6) =694a(7) =1828a(8) =4815a(9) =12867a(10) =34562a(11) =93921a(12) =257222a(13) =711872a(14) =1983045a(15) =5574177a(16) =15766834a(17) =44933155a(18) =128790245a(19) =371524353a(20) =1077235107a(21) =3141337862a(22) =9203553458a(23) =27098846070a(24) =80132014258a(25) =238015962210a(26) =709753556178