### 7.2.9 Bernoulli numbers

The Bernoulli polynomial Bn is defined by:

B0=1, Bn′(x)=n Bn−1(x), | ∫ |
1
0
| Bn(x) d x=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 n, an integer.
- bernoulli(n) returns the nth Bernoulli number, Bn.

#### Example

bernoulli(6)

1
42