G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^4.

Terms

a(0) =1a(1) =3a(2) =7a(3) =22a(4) =97a(5) =469a(6) =2339a(7) =12148a(8) =65295a(9) =358979a(10) =2006977a(11) =11380702a(12) =65311575a(13) =378574425a(14) =2213092750a(15) =13032826536a(16) =77244242937a(17) =460413902079