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

Terms

a(0) =1a(1) =2a(2) =3a(3) =16a(4) =83a(5) =460a(6) =2767a(7) =17210a(8) =110308a(9) =723624a(10) =4832363a(11) =32747106a(12) =224619408a(13) =1556484636a(14) =10879744696a(15) =76621739626a(16) =543159825499