分割数

\[p_{1}\left(n,k,m\right)=p_{1}\left(n,k-1,m\right)+p_{1}\left(n-k,k,m\right)-p_{1}\left(n-k-m,k-1,m\right)\]

\[p\left(n,2\right)=1+\left\lfloor \frac{n}{2}\right\rfloor \]

\[p\left(n,k\right)=p\left(n,k-1\right)+p\left(n-k,k\right)\]

\[q\left(n,k\right)=p\left(n-k,k\right)\]

\[\sum_{k=0}^{\infty}P_{d}\left(k\right)z^{k}=\prod_{k=1}^{\infty}\left(1+z^{k}\right)\]

\[\sum_{k=0}^{\infty}P\left(k\right)z^{k}=\prod_{k=1}^{\infty}\frac{1}{1-z^{k}}\]