Hilbert matrix : hilbert

hilbert takes as argument an integer n.
hilbert returns the Hilbert matrix.
A Hilbert matrix is a square matrix of size n whose elements a_{j, k} are :

a_{j, k} = $${\frac{{1}}{{j+k+1}}}$$,    0 $$\leq$$ j, 0 $$\leq$$ k

Input :

hilbert(4)

Output :

[[1,1/2,1/3,1/4],[1/2,1/3,1/4,1/5],[1/3,1/4,1/5,1/6], [1/4,1/5,1/6,1/7]]