Number of ballot sequences of length n with exactly 3 fixed points.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =1a(5) =3a(6) =9a(7) =28a(8) =93a(9) =321a(10) =1168a(11) =4404a(12) =17328a(13) =70408a(14) =296436a(15) =1284768a(16) =5740804a(17) =26332788a(18) =124066608a(19) =598625296a(20) =2958281328a(21) =14941136784a(22) =77111251408a(23) =406028059968