---
tag: 0SJNCJCCQG
kind: concept
name: Falling factorial
msc: [05A10]
sources:
  - url: https://en.wikipedia.org/wiki/Falling_and_rising_factorials
    locator: lead section
---

## Summary

The falling factorial $(x)_k$ is the product of $k$ consecutive descending factors that start at $x$. It counts ordered selections without repetition, and it is a basis of the polynomials that is useful in finite difference calculus. The node [[falling factorial|0N5M924N3P]] gives the precise definition.