<s>[INST] $n^{\text{th}}$ term of The Maclaurin Expansion of $\dfrac{1}{(1-x)^3(1+x)(1+x+x^2)}$? I am trying to find the coefficient of $n^{\text{th}}$ term of the Maclaurin series of $$\dfrac{1}{(1-x)^3(1+x)(1+x+x^2)}.$$
How can I find the coefficient of $n^{\text{th}}$ term of this function?
 [/INST] As noted by @Daniel, it equals $1/(1-x)(1-x^2)(1-x^3)$.  Another way to put that is $$\frac{(1+x+...+x^5)(1+x^2+x^4)(1+x^3)}{(1-x^6)^3}$$
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