Abstract: For antisymmetrized nth power of representation Γ of a finite group G we define the Molien type generating function M (-) (Γ,G; z) ∑_n=0^∞ C (-)_n1 zⁿ where c (-)_n1 is the multiplicity of the identity representation in the antisymmetrized nth power of representation of finite group G. We obtain a formula for M(-) (Γ,G; z) and two algorithms for its calculations using the characters only.