---
tag: 0JHXPVFKT0
kind: concept
name: Exponential generating function
msc: [05A15]
sources:
  - url: https://en.wikipedia.org/wiki/Generating_function
    locator: Exponential generating function (EGF)
---

## Summary

An exponential generating function encodes a sequence $(a_n)$ as the series $\sum a_n x^n / n!$. It is the natural tool to count labelled structures, because products give binomial convolutions. The node [[exponential generating function|0KE6NBTVY8]] gives the precise definition.