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I wonder what is the generator term (an) for the MacLaurin series of $(1-x^2) /(1+x^3)$.

Thanks, Amin

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    Alternately, the geometric series for $(1+x^3)^{-1}$ and then just multiply. – 2017-02-05
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    By the way, since you seem new, I would like to point out that you can up vote questions and answers you deem good and accept answers to your questions by clicking the buttons on the left side of answers. :-) – 2017-02-06
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    @SimplyBeautifulArt Just did that :) Thanks for your help. – 2017-02-06

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We may use the geometric series:

$$\begin{align}\frac{1-x^2}{1+x^3}&=\frac1{1-(-x^3)}-\frac{x^2}{1-(-x^3)}\\&=\sum_{n=0}^\infty(-x^3)^n-x^2\sum_{k=0}^\infty(-x^3)^k\end{align}$$

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    Yes, but I want the series to appear as a_n * x^n. Could you please elaborate how you end up having a closed form a_n? – 2017-02-06
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    @aminsadeghi I will provide you with a hint. Expand each sum a few terms. The pattern should be obvious. – 2017-02-06
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    Thanks, I actually did that and ended up with: 1 - x^2 - x^3 + x^5 + x^6 - x^8 - x^9 + ..., which I don't have any idea how to make it closed-form :( – 2017-02-06
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    @aminsadeghi Well, for $k=3n+1$, $a_k=0$. For $k=3n$, $a_k=(-1)^k$. For $k=\dots$ can you finish this? – 2017-02-06
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    Oh, perfect. I thought there would be a single closed-form formula :D my bad. Thanks :) – 2017-02-06