Two new forms are given for the Molien (generating) function for multiplicity cn1 of the identity representation in the symmetrized nth power of representation Γ of finite group G. These are M (Γ,G;z) =Σncn1zn=1/‖G‖Σg exp [Σlzlχ (gl)/l] =1/‖G‖ΣgΠj[1−zγj(g)]−δj, where g is an element in G γj(g) an irreducible character in the Abelian subgroup A generated by g, δj the subduction coefficient of Γ of G↓γj of A; we usually take Γ irreducible. These forms have the merit of only requiring characters. In the following paper these algorithms are used to compute the Molien function for space group irreducible representation.