I have an equation of the form [tex](1-x)(1-x^2)(1-x^3)\cdot\cdot\cdot(1-x^n)[/tex]. Or, in maple notation,(adsbygoogle = window.adsbygoogle || []).push({}); product(1-x^a, a=1..n).

I've been trying to find a way to express this as an expanded polynomial in sigma notation so that I can extract coefficients (for an enumerative generating function). If the exponents were all the same then the binomial theorem could be applied, but unfortunately it is not that simple.

I have made little progress towards successfully expanding. I tried reforming it as a different counting problem and solving it indirectly, but still came to this same fundamental problem, just in a different form. However, in doing so, I think I've found a connection to a sum of sums; the answer may involve summing over i=0..n and j=i..n?

Has anyone seen this problem before? Any helpful links?

Thank you very much in advance,

Sane

(P.S. This is not homework. This is extracurricular fun to find a more efficient way to solve a computer science problem I stumbled across a while ago.)

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# Coefficients in expansion of product(1-x^a, a=1n)?

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