Let A = kQ/I be a finite-dimensional Nakayama algebra, where Q is an Euclidean diagram An for some n with cyclic orientation, and I is an admissible ideal generated by a single monomial relation. In this note we determine explicitly all the Hochschild homology and cohomology groups of A based on a detailed description of the Bardzell complex. Moreover, the cyclic homology of A can be calculated in the case that the underlying field is of characteristic zero.