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

s:=6;

rho0:=sigma0(1+x)*log(x+1);

rho1:=series(rho0,x,s+1);

rho2:=convert(rho1,polynom);

rho3:=expand(unapply(rho2,x)(w-1));

beta:=1/coeff(rho3,w,s);

sigma:=beta*sigma0(w);

rho:=beta*rho3;

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

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