Using density functional theory and generalized gradient approximation for exchange-correlation potential, we have calculated the equilibrium geometries and energetics of neutral and negatively charged AlnCu (n=11,12,13,14) clusters. Unlike the alkali atom-doped aluminum clusters in the same size range, the copper atom resides inside the aluminum cluster cage. Furthermore, the 3d and 4s energy levels of Cu hybridize with the valence electrons of Al causing a redistribution of the molecular orbital energy levels of the Al-n clusters. However, this redistribution does not affect the magic numbers of AlnCu clusters that could be derived by assuming that Cu donates one electron to the valence levels of Al-n clusters. This behavior, brought about by the smaller size and large ionization potential of the copper atom, contributes to the anomalous properties of AlnCu- anions: Unlike AlnX- (X=alkali atom), the mass ion intensities of AlnCu- are similar to those of Al-n(-). The calculated adiabatic electron affinities are also in very good agreement with experiment.