Number of ballot sequences of length n with exactly 5 fixed points.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =1a(7) =3a(8) =9a(9) =29a(10) =99a(11) =356a(12) =1343a(13) =5279a(14) =21584a(15) =91324a(16) =399456a(17) =1799568a(18) =8343404a(19) =39702144a(20) =193768604a(21) =967992476a(22) =4946617328a(23) =25817913584a(24) =137549830384a(25) =747137750064