a(n) = [x^n](x - 2*x^3)/(1 - 2*x*(x + 1))^2.

Terms

a(0) =0a(1) =1a(2) =4a(3) =14a(4) =48a(5) =156a(6) =496a(7) =1544a(8) =4736a(9) =14352a(10) =43072a(11) =128224a(12) =379136a(13) =1114560a(14) =3260160a(15) =9494656a(16) =27545600a(17) =79642880a(18) =229573632a(19) =659951104a(20) =1892478976a(21) =5414755328a(22) =15461117952a(23) =44064835584a(24) =125371383808a(25) =356137570304