G.f.: (1-2*x)*sqrt(1-4*x).

Terms

a(0) =1a(1) =-4a(2) =2a(3) =0a(4) =-2a(5) =-8a(6) =-28a(7) =-96a(8) =-330a(9) =-1144a(10) =-4004a(11) =-14144a(12) =-50388a(13) =-180880a(14) =-653752a(15) =-2377280a(16) =-8691930a(17) =-31935960a(18) =-117858900a(19) =-436698240a(20) =-1623971580a(21) =-6059188080a(22) =-22676052360a(23) =-85100059200a(24) =-320188972740