The

Bernoulli numbers were created by Jakob Bernoulli in his

statistical studies. Let

**B**_{0}=1. Then the k

^{th} Bernoulli number

**B**_{k} is recursively defined as:

/ \ / \ / \ / \
| k+1 | B + | k+1 | B + | k+1 | B + | k+1 | B + B = 0
| 1 | k | 2 | k-1 | 3 | k-2 | k | 1 0
\ / \ / \ / \ /
where
/ \
| s | = s!
| r | --------
\ / r!(r-s)!

So,

**B**_{0}=1,

**B**_{1}=-1/2,

**B**_{2}=1/6,

etc.
The Bernoulli numbers define the

irregular primes as well.

*Information gathered from: http://primes.utm.edu/glossary/page.php/BernoulliNumber.html*