Simplifying a short code

[schniefen]

I'm approximating the natural logarithm according to the formulas given in this paper https://www.ams.org/journals/mcom/1972-2...7438-2.pdf (see second page, under 'Algorithm for logarithm'). When evaluating dki one attains a matrix of the form

([[d_00,d_01,d_02,...,d_nn],
  [     d_11,d_12,...,d_nn],
  [               ...,d_nn],
  [          d_n-1n-1,d_nn],
  [                   d_nn]])

Here is the full code.

def ln(x,n):
    a =[(1+x)/2]
    g =[x**(1/2)]
    for i in range(n):
        a.append((a[i]+g[i])/2)
        g.append((a[i+1]*g[i])**(1/2))
    d_0 =[]
    for k in range(n+1):
        d_0.append(a[k])
    d_1=[]
    for k in range (1,n+1):
        d_1.append((d_0[k]-4**(-1)*d_0[k-1])/(1-4**(-1)))
    d_2=[]
    for k in range(2,n+1):
        d_2.append((d_1[k-1]-4**(-2)*d_1[k-2])/(1-4**(-2)))
    d_3=[]
    for k in range(3,n+1):
        d_3.append((d_2[k-2]-4**(-3)*d_2[k-3])/(1-4**(-3)))
    ...
    d_n=[]
    for k in range(n,n+1):
        d_n.append((d_n-1[k-(n-1)]-4**(-n)*d_n-1[k-n])/(1-4**(-n)))
    return (x-1)/d_n[0]