We develop for charmed hadron production in relativistic heavy-ion collisions a comprehensive coalescence model that includes an extensive set of $s$ and $p$-wave hadronic states as well as the strict energy-momentum conservation, which ensures the boost invariance of the coalescence probability and the thermal limit of the produced hadron spectrum. By combining our hadronization scheme with an advanced Langevin-hydrodynamics model that incorporates both elastic and inelastic energy loss of heavy quarks inside the dynamical quark-gluon plasma, we obtain a successful description of the $p_mathrm{T}$-integrated and differential $Lambda_c/D^0$ and $D_s/D^0$ ratios measured at RHIC and the LHC. We find that including the effect of radial flow of the medium is essential for describing the enhanced $Lambda_c/D^0$ ratio observed in relativistic heavy-ion collisions. We also find that the puzzling larger $Lambda_c/D^0$ ratio observed in Au+Au collisions at RHIC than in Pb+Pb collisions at the LHC is due to the interplay between the effects of the QGP radial flow and the charm quark transverse momentum spectrum at hadronization. Our study further suggests that charmed hadrons have larger sizes in medium than in vacuum.
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