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

Terms

a(0) =1a(1) =3a(2) =8a(3) =26a(4) =80a(5) =244a(6) =736a(7) =2200a(8) =6528a(9) =19248a(10) =56448a(11) =164768a(12) =478976a(13) =1387328a(14) =4005376a(15) =11530624a(16) =33107968a(17) =94839552a(18) =271091712a(19) =773380608a(20) =2202374144a(21) =6261404672a(22) =17774206976a(23) =50384312320a(24) =142636515328a(25) =403306786816