Integer Partitions

## A000009 - OEIS

\[p(n) := #\{ (a_{1}, \ldots, a_{k}) \mid \sum_{i=1}^{k}a_{i} = n, k \in \mathbb{N} \} .\] \[\begin{eqnarray} (1 + x^{1} + x^{2} + \cdots) (1 + x^{2} + x^{4} + \cdots) (1 + x^{3} + x^{3} + \cdots) \cdots & = & \frac{ 1 }{ 1 - x } \frac{ 1 }{ 1 - x^{2} } \frac{ 1 }{ 1 - x^{3} } \cdots \\ & = & \sum_{n=0}^{\infty} p(n) x^{n} \end{eqnarray}\]

Distinct

• A111133 - OEIS

Reference

• https://www2.math.upenn.edu/~wilf/PIMS/PIMSLectures.pdf
• Partition (number theory) - Wikipedia
• Number of partitions of an integer into distinct parts: Introduction to partitions
• partitions.pdf