[math-fun] Names of coefficients?

Consider the polynomial p(x)=(x-1)^6. For the coefficient of x^3, Macsyma/Maxima returns coeff(p(x),x,3)=-20 (at least after expanding p(x). I would rather have coefficients that are divided by the appropriate binomial coefficient, and whose sign is multiplied by (-1)^(n-i) for the coeff(p(x),x,i), where p(x) is a monic polynomial of degree n. Is there a standard name for these coefficients? Some of the 19th century texts tend to use this type of notation, but I don't know what the modern name for these coefficients is.