  Let $F(x)=\sum\limits_{n=1}^\infty\tau(n)x^n$ be the generating function for
the number $\tau(n)$ of spanning trees in the circulant graphs
$C_{n}(s_1,s_2,\ldots,s_k).$ We show that $F(x)$ is a rational function with
integer coefficients satisfying the property $F(x)=F(1/x).$ A similar result is
also true for the circulant graphs of odd valency
$C_{2n}(s_1,s_2,\ldots,s_k,n).$ We illustrate the obtained results by a series
of examples.
