Suppose I have the following polynomial, $$f(x)=(1+x)^2(1+x+x^2+x^3)^2$$ expanding this gives: $$f(x)=1+4x+8x^2+12x^3+14x^4+12x^5+8x^6+4x^7+x^8$$ now suppose I want to extend this as follow: $$f(x)=(1+x)^2(1+x+x^2+\cdots+x^n)^{n-1}$$ where $n$ is a positive integers and can be odd/even, I wonder how to write the coefficients analytically in terms of $n$?
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5you have the geometric series in the second bracket – Milan Jun 03 '19 at 17:03
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1Writing coefficients in terms of $n$ and expressing $f(x)$ in closed form are two different things. The comment above (+1) does the latter, not the former. – Macavity Jun 03 '19 at 17:08
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@Macavity indeed I need the coefficients in term of $n$. – Wiliam Jun 04 '19 at 10:36
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I have edited the question. – Wiliam Jun 04 '19 at 10:37