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

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =15a(5) =36a(6) =91a(7) =232a(8) =603a(9) =1585a(10) =4213a(11) =11298a(12) =30537a(13) =83097a(14) =227475a(15) =625992a(16) =1730787a(17) =4805595a(18) =13393689a(19) =37458330a(20) =105089229a(21) =295673994a(22) =834086421a(23) =2358641376a(24) =6684761125a(25) =18985057351a(26) =54022715451a(27) =154000562758a(28) =439742222071