---
tag: 0JCQGPY8Z4
kind: concept
name: Stirling numbers of the second kind
msc: [11B73]
sources:
  - url: https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
    locator: Definition
same_as:
  wikidata: Q2601117
  wikipedia: Stirling numbers of the second kind
---

## Summary

The Stirling numbers of the second kind $S(n, k)$ count the partitions of an $n$-element set into $k$ nonempty blocks. They connect ordinary powers with falling factorials and they sum to the Bell numbers. The node [[Stirling numbers of the second kind|0ZN07RQ3JS]] gives the precise definition.