a(n) = [x^(2*n)] ((1 + x)/(1 - x))^n.

Terms

a(0) =1a(1) =2a(2) =16a(3) =146a(4) =1408a(5) =14002a(6) =142000a(7) =1459810a(8) =15158272a(9) =158611106a(10) =1669752016a(11) =17664712562a(12) =187641279616