[x^(n+1)]Reversion[x*(1-x)/(1-3*x)].

Terms

a(0) =1a(1) =-2a(2) =2a(3) =2a(4) =-10a(5) =6a(6) =42a(7) =-102a(8) =-82a(9) =782a(10) =-814a(11) =-3854a(12) =12454a(13) =5014a(14) =-98694a(15) =142218a(16) =472158a(17) =-1932258a(18) =-19038a(19) =14816994a(20) =-27370410a(21) =-64159962a(22) =334154442a(23) =-121279878a(24) =-2418497010a(25) =5523511086a(26) =8914677362a(27) =-61259567662a(28) =44249714438