a(n) is the number of subsets of {1..n} that contain exactly 2 odd and 3 even numbers.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =3a(7) =6a(8) =24a(9) =40a(10) =100a(11) =150a(12) =300a(13) =420a(14) =735a(15) =980a(16) =1568a(17) =2016a(18) =3024a(19) =3780a(20) =5400a(21) =6600a(22) =9075a(23) =10890a(24) =14520a(25) =17160a(26) =22308a(27) =26026a(28) =33124a(29) =38220