Number of ballot sequences of length n with exactly 2 fixed points.

Terms

a(0) =0a(1) =0a(2) =1a(3) =1a(4) =3a(5) =8a(6) =24a(7) =74a(8) =246a(9) =848a(10) =3088a(11) =11644a(12) =45844a(13) =186336a(14) =784928a(15) =3403128a(16) =15212744a(17) =69802944a(18) =328988096a(19) =1587831568a(20) =7848954928a(21) =39651793024a(22) =204691645824