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

Terms

a(0) =1a(1) =3a(2) =10a(3) =57a(4) =378a(5) =2730a(6) =20853a(7) =165592a(8) =1353297a(9) =11307168a(10) =96148149a(11) =829336122a(12) =7238765532a(13) =63816716547a(14) =567425771478