# The n-th Bernoulli number: bernoulli

### 5.7.9 The n-th Bernoulli number: bernoulli

The Bernoulli polynomial Bn is defined by:

B0=1, Bn′(x)=nBn−1(x),

∫

1
0

Bn(x)dx=0

The nth Bernoulli number is Bn = Bn(0), and is also given by the formula:

t
et−1

=

+∞
∑
n=0

B(n)
n!

tn

The bernoulli command computes the Bernoulli numbers.

- bernoulli takes one argument:
  n, an integer.
- bernoulli(n) returns the n-th Bernoulli number, Bn.

#### Example.

Input:

bernoulli(6)

Output:

1
42