Abel polynomials

The Abel polynomials are a sequence of polynomials named after Niels Henrik Abel, defined by the following equation:


 * $$p_n(x)=x(x-an)^{n-1}$$

This polynomial sequence is of binomial type: conversely, every polynomial sequence of binomial type may be obtained from the Abel sequence using umbral calculus.

Examples
For $a = 1$, the polynomials are


 * $$p_0(x)=1;$$
 * $$p_1(x)=x;$$
 * $$p_2(x)=-2x+x^2;$$
 * $$p_3(x)=9x-6x^2+x^3;$$
 * $$p_4(x)=-64x +48x^2-12x^3+x^4;$$

For $a = 2$, the polynomials are


 * $$p_0(x)=1;$$
 * $$p_1(x)=x;$$
 * $$p_2(x)=-4x+x^2;$$
 * $$p_3(x)=36x-12x^2+x^3;$$
 * $$p_4(x)=-512x +192x^2-24x^3+x^4;$$
 * $$p_5(x)=10000x-4000x^2+600x^3-40x^4+x^5;$$
 * $$p_6(x)=-248832x+103680x^2-17280x^3+1440x^4-60x^5+x^6;$$