restart;
# Backwards Differentiation Formula
sigma0:=w->w^s;

s:=6;

logseries:=convert(subs(v=1/w-1,series(log(1+v),v,s+1)),polynom);

rho0:=-simplify(sigma0(w)*logseries);

beta:=1/coeff(rho0,w,s);

sigma:=beta*sigma0(w);

rho:=beta*rho3;

R:=[solve(rho=0)];

seq(abs(evalf(R[i])),i=1..s);