The square-planar layered nickelates Rₙ₊₁NiₙO₂ₙ₊₂ (R= Nd, n=4-7) have been recently shown to be superconducting without the need for chemical doping or pressure. Here, we examine the electronic structure of the analog higher-order square-planar palladates --that have not yet been synthesized-- via ab initio calculations. These layered palladates exhibit larger bandwidths, an increased p-d hybridization, and less interference from R-d bands at the Fermi level. These characteristics make them closer cuprate analogs and promising candidates to pursue in the context of unconventional superconductivity.