G.f. satisfies A^3 = BINOMIAL(A^2).

Terms

a(0) =1a(1) =1a(2) =3a(3) =15a(4) =108a(5) =1032a(6) =12388a(7) =179572a(8) =3052986a(9) =59555338a(10) =1310677726a(11) =32114051862a(12) =866766965308