  We determine the improvement factor $c_{SW}$ in one-loop lattice perturbation
theory for the plaquette and Symanzik improved gauge actions. The fermionic
action is ${\mathcal{O}(a)}$ clover improved with one-time stout smearing.
$c_{SW}$ is derived from the one-loop correction to the quark-quark-gluon
vertex in the off-shell regime. We give a first numerical value for the
one-loop contribution to the non gauge-invariant improvement coefficient
$c_{NGI}$ for the quark field using the plaquette action. A discussion of mean
field improvement is included.
