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

Terms

a(0) =0a(1) =1a(2) =5a(3) =16a(4) =42a(5) =100a(6) =228a(7) =512a(8) =1144a(9) =2544a(10) =5616a(11) =12288a(12) =26656a(13) =57408a(14) =122944a(15) =262144a(16) =556928a(17) =1179392a(18) =2490112a(19) =5242880a(20) =11010560a(21) =23069696a(22) =48235520a(23) =100663296a(24) =209713152a(25) =436203520a(26) =905965568a(27) =1879048192a(28) =3892322304a(29) =8053080064