a(n) is the number of subsets of {1..n} that contain 3 even and 3 odd numbers.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =1a(7) =4a(8) =16a(9) =40a(10) =100a(11) =200a(12) =400a(13) =700a(14) =1225a(15) =1960a(16) =3136a(17) =4704a(18) =7056a(19) =10080a(20) =14400a(21) =19800a(22) =27225a(23) =36300a(24) =48400a(25) =62920a(26) =81796a(27) =104104a(28) =132496a(29) =165620