  A search for Higgs boson pair (HH) production with one Higgs boson decaying
to two bottom quarks and the other to two W bosons are presented. The search is
done using proton-proton collisions data at a centre-of-mass energy of 13 TeV,
corresponding to an integrated luminosity of 138 fb$^{-1}$ recorded by the CMS
detector at the LHC from 2016 to 2018. The final states considered include at
least one leptonically decaying W boson. No evidence for the presence of a
signal is observed and corresponding upper limits on the HH production cross
section are derived. The limit on the inclusive cross section of the
nonresonant HH production, assuming that the distributions of kinematic
observables are as expected in the standard model (SM), is observed (expected)
to be 14 (18) times the value predicted by the SM, at 95% confidence level. The
limits on the cross section are also presented as functions of various Higgs
boson coupling modifiers, and anomalous Higgs boson coupling scenarios. In
addition, limits are set on the resonant HH production via spin-0 and spin-2
resonances within the mass range 250-900 GeV.
