  We introduce higher dimensional analogues of the Nakayama algebras from the
viewpoint of Iyama's higher Auslander--Reiten theory. More precisely, for each
Nakayama algebra $A$ and each positive integer $d$, we construct a finite
dimensional algebra $A^{(d)}$ having a distinguished $d$-cluster-tilting
$A^{(d)}$-module whose endomorphism algebra is a higher dimensional analogue of
the Auslander algebra of $A$. We also construct higher dimensional analogues of
the mesh category of type $\mathbb{ZA}_\infty$ and the tubes.
