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2.8.9  The n-th Bernoulli number : bernoulli

bernoulli takes as argument an integer n.
bernoulli returns the n-th Bernoulli number B(n).
The Bernoulli numbers are defined by :

t
et−1
=
+∞
n=0
 
B(n)
n!
tn 

Bernoulli polynomials Bk are defined by :

B0=1,    Bk′(x)=kBk−1(x),     
1


0
Bk(x)dx=0 

and the relation B(n)=Bn(0) holds.
Input :

bernoulli(6)

Output :

1/42

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