---
tag: 0JPH2Y4DFV
kind: concept
name: Central binomial coefficient
msc: [05A10]
sources:
  - url: https://en.wikipedia.org/wiki/Central_binomial_coefficient
    locator: lead section
same_as:
  wikidata: Q1045966
  wikipedia: Central binomial coefficient
---

## Summary

The central binomial coefficients $\binom{2n}{n}$ are the middle entries of the even rows of Pascal's triangle. They count balanced lattice paths and appear in the formula for Catalan numbers. The node [[central binomial coefficient|01WHD9T0V6]] gives the precise definition.