  The results of analytical approximations and extensive calculations based on
a path integral Monte Carlo (PIMC) scheme are presented. A new (direct) PIMC
method allows for a correct determination of thermodynamic properties such as
energy and equation of state of dense degenerate Coulomb systems. In this
paper, we present results for dense partially ionized hydrogen at intermediate
and high temperature. We give a quantitative comparison with the available
results of alternative (restricted) PIMC simulations and with analytical
expressions based on iterpolation formulas meeting the exact limits at low and
high densities. Good agreement between the two simulations is found up to
densities of the order of $10^{24}cm^{-3}$. The agreement with the analytical
results is satisfactory up to densities in the range $10^{22}...
10^{23}cm^{-3}$.
