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The Bernoulli numbers were created by Jakob Bernoulli in his statistical studies. Let B0=1. Then the kth Bernoulli number Bk 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, B0=1, B1=-1/2, B2=1/6, etc.

The Bernoulli numbers define the irregular primes as well.
Information gathered from: http://primes.utm.edu/glossary/page.php/BernoulliNumber.html

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