  This paper is contributed to a fast algorithm for Hankel tensor-vector
products. For this purpose, we first discuss a special class of Hankel tensors
that can be diagonalized by the Fourier matrix, which is called
\emph{anti-circulant} tensors. Then we obtain a fast algorithm for Hankel
tensor-vector products by embedding a Hankel tensor into a larger
anti-circulant tensor. The computational complexity is about $\mathcal{O}(m^2 n
\log mn)$ for a square Hankel tensor of order $m$ and dimension $n$, and the
numerical examples also show the efficiency of this scheme. Moreover, the block
version for multi-level block Hankel tensors is discussed as well. Finally, we
apply the fast algorithm to exponential data fitting and the block version to
2D exponential data fitting for higher performance.
