  The recent observation of superconductivity in an infinite-layer and
quintuple-layer nickelate within the same $R_{n+1}$Ni$_{n}$O$_{2n+2}$ series
($R$ = rare-earth, $n=2-\infty$, with $n$ indicating the number of NiO$_{2}$
layers along the $c$-axis), unlocks their potential to embody a whole family of
unconventional superconductors. Here, we systematically investigate the
many-body electronic structure of the layered nickelates (with $n=2-6,\infty$)
within a density-functional theory plus dynamical mean-field theory framework
and contrast it with that of the known superconducting members of the series
and with the cuprates. We find that many features of the electronic structure
are common to the entire nickelate series, namely, strongly correlated
Ni-$d_{x^{2}-y^{2}}$ orbitals that dominate the low-energy physics, mixed
Mott-Hubbard/charge-transfer characteristics, and $R$($5d$) orbitals acting as
charge reservoirs. Interestingly, we uncover that the electronic structure of
the layered nickelates is highly tunable as the dimensionality changes from
quasi-two-dimensional to three-dimensional as $n \rightarrow \infty$.
Specifically, we identify the tunable electronic features to be: the
charge-transfer energy, presence of $R(5d)$ states around the Fermi level, and
the strength of electronic correlations.
