  Measurements are presented of associated production of a W boson and a charm
quark (W+c) in proton-proton collisions at a center-of-mass energy of 13 TeV.
The data correspond to an integrated luminosity of 35.7 fb$^{-1}$ collected by
the CMS experiment at the CERN LHC. The W bosons are identified by their decay
into a muon and a neutrino. The charm quarks are tagged via the full
reconstruction of D$^*$(2010)$^\pm$ mesons that decay via D$^*$(2010)$^\pm \to$
D$^0$ + $\pi^\pm \to$ K$^{\mp}$ + $\pi^\pm$ + $\pi^\pm$. A cross section is
measured in the fiducial region defined by the muon transverse momentum
$p_{T}^{\mu} >$ 26 GeV, muon pseudorapidity $|\eta^{\mu}| <$ 2.4, and charm
quark transverse momentum $p_{T}^{c} >$ 5 GeV. The inclusive cross section for
this kinematic range is $\sigma$(W+c) = 1026 $\pm$ 31 (stat)
$\substack{+76\\-72}$ (syst) pb. The cross section is also measured
differentially as a function of the pseudorapidity of the muon from the W boson
decay. These measurements are compared with theoretical predictions and are
used to probe the strange quark content of the proton.
