Yoshikawa constructed an invariant of 2-elementary K3 surfaces by using equivariant analytic torsion. He also proved that the invariant is expressed as the Petersson norm of a certain automorphic form on a bounded symmetric domain of type IV and a certain Siegel modular form. In this talk, we generalize this result to a class of higher dimensional manifolds. More precisely, we construct an invariant of irreducible holomorphic symplectic manifolds which are deformation equivalent to the Hilbert scheme of two points of a K3 surface with antisymplectic involution by using equivariant analytic torsion. In addition, we show that the invariant is expressed as the Petersson norm of a certain automorphic form on a bounded symmetric domain of type IV and a certain Siegel modular form in some cases.