The
Bernoulli numbers were created by Jakob Bernoulli in his
statistical studies. Let
B0=1. Then the k
th 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