  An \emph{$(r,k)$-parking function} of length $n$ may be defined as a sequence
$(a_1,\dots,a_n)$ of positive integers whose increasing rearrangement
$b_1\leq\cdots\leq b_n$ satisfies $b_i\leq k+(i-1)r$. The case $r=k=1$
corresponds to ordinary parking functions. We develop numerous properties of
$(r,k)$-parking functions. In particular, if $F_n^{(r,k)}$ denotes the
Frobenius characteristic of the action of the symmetric group $\mathfrak{S}_n$
on the set of all $(r,k)$-parking functions of length $n$, then we find a
combinatorial interpretation of the coefficients of the power series $\left(
\sum_{n\geq 0}F_n^{(r,1)}t^n\right)^k$ for any $k\in \mathbb{Z}$. When $k>0$,
this power series is just $\sum_{n\geq 0} F_n^{(r,k)} t^n$; when $k<0$, we
obtain a dual to $(r,k)$-parking functions. We also give a $q$-analogue of this
result. For fixed $r$, we can use the symmetric functions $F_n^{(r,1)}$ to
define a multiplicative basis for the ring $\Lambda$ of symmetric functions. We
investigate some of the properties of this basis.
