Letp(n) denote the number of partitions ofn. A new infinite family of inequalities forp(n) is presented. This generalizes a result by William Chen et al. From this infinite family, another infinite family of inequalities for\documentclass[12pt]{minimal}
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				\begin{document}$$\log p(n)$$\end{document}logp(n)is derived. As an application of the latter family one, for instance obtains that for\documentclass[12pt]{minimal}
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				\begin{document}$$n\ge 120$$\end{document}n≥120,\documentclass[12pt]{minimal}
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				\begin{document}$$\begin{aligned} p(n)^2>\Biggl (1+\frac{\pi }{\sqrt{24}n^{3/2}}-\frac{1}{n^2}\Biggr )p(n-1)p(n+1). \end{aligned}$$\end{document}p(n)2>(1+π24n3/2-1n2)p(n-1)p(n+1).