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

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =2a(5) =5a(6) =14a(7) =35a(8) =132a(9) =399a(10) =1556a(11) =5346a(12) =21515a(13) =82940a(14) =351298a(15) =1470859a(16) =6559568a(17) =29273847a(18) =137203616a(19) =647330760a(20) =3177545635a(21) =15754135608a(22) =80674471962a(23) =418173444944