G.f. satisfies A(x) = 1/(1-x)^3 + x*A(x)^3.

Terms

a(0) =1a(1) =4a(2) =18a(3) =112a(4) =847a(5) =7086a(6) =62974a(7) =583002a(8) =5560323a(9) =54249583a(10) =538873135a(11) =5431177821a(12) =55402340842a(13) =570899082760