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In this paper, we study a family of single variable integral representationsfor some products of $\zeta(2n+1)$, where $\zeta(z)$ is Riemann zeta functionand $n$ is positive integer. Such representation involves the integral$Lz(a,b):=\frac{1}{(a-1)!b!}\int_{0}^{1}\log^a (t)\log^b (1-t)dt/t$ withpositive integers $a,b$, which is related to Nielsen's generalizedpolylogarithms. By analyzing the related partition problem, we discuss thestructure of such integral representation, especially the condition ofexpressing products of $\zeta(2n+1)$ by finite $\mathbb{Q}(\pi)$-linearcombination of $Lz(a,b)$.

On Some Integral Representation Of $\zeta(n)$ Involving Nielsen's Generalized Polylogarithms And The Related Partition Problem