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 :

$${\frac{{t}}{{e^t-1}}}$$ = $$\sum_{{n=0}}^{{+\infty}}$$$${\frac{{B(n)}}{{n!}}}$$tⁿ

Bernoulli polynomials B_k are defined by :

B₀ = 1,    B_k'(x) = kB_k-1(x),    $$\int_{0}^{1}$$B_k(x)dx = 0

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

bernoulli(6)

Output :

1/42