Calculate the coefficients of order l numerical derivative using Fornberg 's method

f^(l) (x) = [a f(x - k h) + b f(x - (k-1) h) + ... + p f(x + (n-1) h) + q f(x + n h)]/h^l

k = 0;
n = 2;
l = 1; (* order of the derivative *)
m = k + n ; (* number of terms less 1 *)
CoefficientList[Normal[Series[u^k*(Log[u])^l,{u,1,m}]],u]