  In this paper, we study a family of single variable integral representations
for some products of $\zeta(2n+1)$, where $\zeta(z)$ is Riemann zeta function
and $n$ is positive integer. Such representation involves the integral
$Lz(a,b):=\frac{1}{(a-1)!b!}\int_{0}^{1}\log^a (t)\log^b (1-t)dt/t$ with
positive integers $a,b$, which is related to Nielsen's generalized
polylogarithms. By analyzing the related partition problem, we discuss the
structure of such integral representation, especially the condition of
expressing products of $\zeta(2n+1)$ by finite $\mathbb{Q}(\pi)$-linear
combination of $Lz(a,b)$.
