We present results of a simulation of QCD on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice with 2 continuum flavors of a $p4$-improved staggered fermion with mass $m/T=0.4.$ Derivatives of the thermodynamic grand potential $\ensuremath{\Omega}$ with respect to the quark chemical potential ${\ensuremath{\mu}}_{q}$ up to fourth order are calculated, enabling estimates of the pressure, quark number density and associated susceptibilities as functions of ${\ensuremath{\mu}}_{q}$ via Taylor series expansion. Discretization effects associated with various staggered fermion formulations are discussed in some detail. In addition it is possible to estimate the radius of convergence of the expansion as a function of temperature. We also discuss the calculation of energy and entropy densities which are defined via mixed derivatives of $\ensuremath{\Omega}$ with respect to the bare couplings and quark masses.