---
tag: 0KY7GS695G
kind: concept
name: Stirling numbers of the first kind
msc: [11B73]
sources:
  - url: https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
    locator: Definition by permutation
same_as:
  wikidata: Q2657556
  wikipedia: Stirling numbers of the first kind
---

## Summary

The Stirling numbers of the first kind count the permutations of $n$ elements with exactly $k$ cycles. They are the coefficients of the rising and falling factorials as polynomials. The node [[Stirling numbers of the first kind|0Z22VQH17V]] gives the precise definition.