# Two new explicit formulas for the Bernoulli Numbers

## TL;DR

This paper introduces two novel explicit formulas for Bernoulli Numbers involving Stirling and Eulerian Numbers, expanding the mathematical tools available for their computation.

## Contribution

The paper presents two new explicit formulas for Bernoulli Numbers using Stirling and Eulerian Numbers, which are claimed to be novel contributions.

## Key findings

- Two new formulas for Bernoulli Numbers are derived.
- Additional formulas, likely known, are also presented.
- Formulas relate Bernoulli Numbers to Stirling and Eulerian Numbers.

## Abstract

In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more probably known formulas.