Higman's PORC theorem for Frattini class two

Statement
Define $$F(p,n)$$ as the number of isomorphism classes of groups of order $$p^n$$ that have Frattini class two, in the sense that the Frattini subgroup is a central subgroup and is elementary abelian. Then, for any fixed $$n$$, $$F(p,n)$$ is a PORC function of $$p$$, i.e., it is a polynomial on residue classes.