<s>[INST] Find the sequence $a_k$ for generating function $\left(\frac{1-x^3}{1-x}\right)^n$ We know that $\frac{1}{(1-x)^n} = \sum_{k=0}^\infty \binom{k+n-1}{n-1} x^k$
I also worked out $(1-x^3)^n$ using the binomial theorem and got $(1-x^3)^n = \sum_{i=0}^\infty (-1)^i \binom{n}{n-i} x^{3i}$
I'm not sure what to do with these to get $a_k$ from $\sum_{k=0}^\infty a_k x^k$ or if these are even what I need to solve the problem
Any help is appreciated
 [/INST] Hint:
\begin{align*}
\left(\frac{1-x^3}{1-x}\right)^n=\left(\frac{(1-x)\left(1+x+x^2\right)}{1-x}\right)^n=\left(1+x+x^2\right)^n
\end{align*}
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