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

Terms

a(0) =1a(1) =3a(2) =14a(3) =94a(4) =735a(5) =6239a(6) =55888a(7) =520028a(8) =4977321a(9) =48689260a(10) =484623552a(11) =4892304686a(12) =49971163021a(13) =515496741918