# Finding the co-efficient of $x^{10}$ in $\frac{1}{(1-x^{10})(1-x^5)(1-x^2)(1-x)}$

While trying to solve a problem with from STEP questions, I encountered this. I am not sure whether this approach is right for that question but this doesn't look like the right way to approach. Any information would be helpful.

• what is "this" approach? perhaps you meant to have a hyperlink? – R_D Oct 19 '15 at 8:50
• What is the denominator in 1/(1-x^10)(1-x^5)(1-x^2)(1-x)? – A.Γ. Oct 19 '15 at 8:51
• Use $\frac{1}{1-y} = 1 + y + y^2 + y^3+....$ and then just count who will give you the required index. – Shailesh Oct 19 '15 at 8:52
• While we wait for Shailesh to find the time you can study generatingfunctionology and some examples such as this, this or this. Plenty of other good examples. – Jyrki Lahtonen Oct 19 '15 at 9:28
• This is also something that might be interesting in connection with this question. Maybe that coin problem is the origin? – mickep Oct 19 '15 at 9:35