  This Letter describes measurements of inclusive W (--> e nu) + n jet cross
sections (n = 1-4), presented as total inclusive cross sections and
differentially in the nth jet transverse momentum. The measurements are made
using data corresponding to an integrated luminosity of 4.2 fb-1 collected by
the D0 detector at the Fermilab Tevatron Collider, and achieve considerably
smaller uncertainties on W +jets production cross sections than previous
measurements. The measurements are compared to next-to-leading order
perturbative QCD (pQCD) calculations in the n =1-3 jet multiplicity bins and to
leading order pQCD calculations in the 4-jet bin. The measurements are
generally in agreement with pQCD predictions, although certain regions of phase
space are identified where the calculations could be improved.
