# Generating function into polynomail

i) Find a generating function expression of a sequence with terms $$d_n=\sum_{p=0}^n p^3$$ using operations on the geometric series $$\sum_{n\geq 0} x^n$$

ii) Derive a polynomial (in $$n$$) expression for $$d_n$$.

for i) I got $$x(1+4x+x^2)/(1-x)^5$$ but I'm confused what to do for ii), how does one derive that?

$$\frac{1}{(1-x)^5} = (1-x)^{-5}=\sum_{n=0}^{\infty} \binom{n+4}{4} x^n$$ by the Binomial Theorem.