Number of ballot sequences of length n with exactly 7 fixed points.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =1a(8) =1a(9) =3a(10) =9a(11) =29a(12) =99a(13) =357a(14) =1351a(15) =5342a(16) =21983a(17) =93823a(18) =414198a(19) =1886424a(20) =8846390a(21) =42628782a(22) =210773592a(23) =1067599984a(24) =5533263752a(25) =29307314408a(26) =158484944416a(27) =874103230896