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6.7.9  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.


Example.
Input:

bernoulli(6)

Output:

1
42

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