  We use on-shell recursion relations to compute analytically the one-loop
corrections to maximally-helicity-violating n-gluon amplitudes in QCD. The
cut-containing parts have been computed previously; our work supplies the
remaining rational parts for these amplitudes, which contain two gluons of
negative helicity and the rest positive, in an arbitrary color ordering. We
also present formulae specific to the six-gluon cases, with helicities (- + - +
+ +) and (- + + - + +), as well as numerical results for six, seven, and eight
gluons. Our construction of the n-gluon amplitudes illustrates the relatively
modest growth in complexity of the on-shell-recursive calculation as the number
of external legs increases. These amplitudes add to the growing body of
one-loop amplitudes known for all n, which are useful for studies of general
properties of amplitudes, including their twistor-space structure.
