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The coefficients of the monomials $u_1^{e_1}u_2^{e_2} \ldots u_n^{e_n}$ of the partition polynomials (ParPs) $[M=M1]$ on pg. 831 of The Handbook of Mathematical Functions by Abramowitz and Stegun are ...

Let $p(n)$ denote the number of (unrestricted) integer partition of $n$ which has the product generating function $$\sum_{n\geq0}p(n)\,x^n=\prod_{j\geq1}\frac1{1-x^j}.$$ On the other hand, for the ...

Let $\lambda$ and $\sigma$ be partitions of $n$: $\lambda_1+\lambda_2+\cdots+\lambda_l=n$ and $\sigma_1+\sigma_2+\cdots+\sigma_s=n$ Let $M_{\lambda \sigma}$ be the number of ways to colour the parts ...