a(n) is the number of subsets of {1..n} that contain 4 even and 4 odd numbers.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =0a(8) =1a(9) =5a(10) =25a(11) =75a(12) =225a(13) =525a(14) =1225a(15) =2450a(16) =4900a(17) =8820a(18) =15876a(19) =26460a(20) =44100a(21) =69300a(22) =108900a(23) =163350a(24) =245025a(25) =353925a(26) =511225a(27) =715715a(28) =1002001a(29) =1366365