Number of ballot sequences of length n with exactly 8 fixed points.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =0a(8) =1a(9) =1a(10) =3a(11) =9a(12) =29a(13) =99a(14) =357a(15) =1351a(16) =5343a(17) =21992a(18) =93912a(19) =414848a(20) =1891264a(21) =8878972a(22) =42849860a(23) =212214460a(24) =1077052284a(25) =5594301872a(26) =29704267536a(27) =161055535088a(28) =890880956848