Number of ballot sequences of length n having 4 largest parts.

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =14a(5) =42a(6) =90a(7) =165a(8) =737a(9) =3003a(10) =15652a(11) =55965a(12) =236924a(13) =851224a(14) =3872838a(15) =16766607a(16) =83026979a(17) =390791373a(18) =1941965432a(19) =9380708953a(20) =47629991554a(21) =241035098010