Multiple exciton generation and recombination (MEG and MER) dynamics in semiconductor quantum dots (QDs) are simulated using ab initio time-dependent density functional theory in combination with nonadiabatic molecular dynamics. The approach differs from other MEG and MER theories because it provides atomistic description, employs time-domain representation, allows for various dynamical regimes, and includes electron-phonon interactions. MEG rapidly accelerates with energy, reflecting strong energy dependence of double exciton (DE) density of states. At early times, MEG is Gaussian rather than exponential. Exponential dynamics, assumed in rate theories, starts at a later time and becomes more important in larger QDs. Phonon-assisted MEG is observed at energies below the purely electronic threshold, particularly in the presence of high-frequency ligand vibrations. Coupling to phonons is essential for MER since higher-energy DEs must relax to recombine into single excitons (SEs), and SEs formed during MERs must lose some of their energy to avoid recreating DEs. MER simulated starting from a DE is significantly slower than MER involving an optical excitation of a SE, followed by MEG and then MER. The latter time scale agrees with experiment, emphasizing the importance of quantum-mechanical superpositions of many DEs for efficient MER. The detailed description of the interplay between MEG and MER coupled to phonons provides important insights into the excited state dynamics of semiconductor QDs and nanoscale materials in general.