a(n) is the number of subsets of {1..n} that contain 5 even and 5 odd numbers.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =0a(8) =0a(9) =0a(10) =1a(11) =6a(12) =36a(13) =126a(14) =441a(15) =1176a(16) =3136a(17) =7056a(18) =15876a(19) =31752a(20) =63504a(21) =116424a(22) =213444a(23) =365904a(24) =627264a(25) =1019304a(26) =1656369a(27) =2576574a(28) =4008004a(29) =6012006