The A${\mathrm{CuO}}_{2}$ compounds---containing only ${\mathrm{CuO}}_{2}$ planes separated by A ions---are the basic ``building blocks'' of the more complex high-${\mathit{T}}_{\mathit{c}}$ superconductors. Trivalently doped ${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{Nd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{CuO}}_{2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ thin films are shown to superconduct with the appearance of a phonon-drag contribution to the thermopower at the superconducting doping threshold. A monotonic increase in this phonon-drag contribution with ${\mathit{T}}_{\mathit{c}}$ suggests that electron-phonon interactions play an important role in the pairing mechanism. A correlation between the deduced BCS coupling constants and ${\mathit{T}}_{\mathit{c}}$ is consistent with strong-coupling theory.