  Generalized Pl\"ucker numbers are defined to count certain types of tangent
lines of generic degree $d$ complex projective hypersurfaces. They can be
computed by identifying them as coefficients of GL(2)-equivariant cohomology
classes of certain invariant subspaces, the so-called coincident root strata,
of the vector space of homogeneous degree $d$ complex polynomials in two
variables. In an earlier paper L\'aszl\'o M. Feh\'er and the author gave a new,
recursive method for calculating these classes. Using this method, we showed
that -- similarly to the classical Pl\"ucker formulas counting the bitangents
and flex lines of a degree $d$ plane curve -- generalized Pl\"ucker numbers are
polynomials in the degree $d$.
  In this paper, by further analyzing our recursive formula, we determine the
leading terms of all the generalized Pl\"ucker formulas.
