For example, according to Stanley the identity $n \cdot \text{pp}(n) = \sum_{i=1}^{n} \sigma_2(i) \text{pp}(n-i)$ has no known bijective proof, where $\text{pp}(n)$ denotes the number of plane partitions of $n$.

For example, according to Stanley the identity $n \cdot \text{pp}(n) = \sum_{i=1}^{n} \sigma_2(i) \text{pp}(n-i)$ has no known bijective proof, where $\text{pp}(n)$ denotes the number of plane partitions of $n$.