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Superconducting nickelates are a new family of strongly correlated electron materials with a phase diagram closely resembling that of superconducting cuprates. While analogy with the cuprates is natural, very little is known about the metallic state of the nickelates, making these comparisons difficult. We probe the electronic dispersion of thin-film superconducting five-layer (n=5) and metallic three-layer (n=3) nickelates by measuring the Seebeck coefficient S. We find a temperature-independent and negative S/T for both n=5 and n=3 nickelates. These results are in stark contrast to the strongly temperature-dependent S/T measured at similar electron filling in the cuprate La_{1.36}Nd_{0.4}Sr_{0.24}CuO_{4}. The electronic structure calculated from density-functional theory can reproduce the temperature dependence, sign, and amplitude of S/T in the nickelates using Boltzmann transport theory. This demonstrates that the electronic structure obtained from first-principles calculations provides a reliable description of the fermiology of superconducting nickelates and suggests that, despite indications of strong electronic correlations, there are well-defined quasiparticles in the metallic state. Finally, we explain the differences in the Seebeck coefficient between nickelates and cuprates as originating in strong dissimilarities in impurity concentrations. Our study demonstrates that the high elastic scattering limit of the Seebeck coefficient reflects only the underlying band structure of a metal, analogous to the high magnetic field limit of the Hall coefficient. This opens a new avenue for Seebeck measurements to probe the electronic band structures of relatively disordered quantum materials.