I got $$(x+x^2+x^3+x^4+x^5)^4=x^4((1-x^5)/1-x)^4$$ and $$(1+x+x^2+...)^4=1/(1-x)^4,$$ what I should do next? Please help me with it, thank you.
2026-04-06 16:57:07.1775494627
What is the coefficient of $x^{11}$ in $(x+x^2+x^3+x^4+x^5)^4(1+x+x^2+...)^4$?
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Write the $x^n$ coefficient in $f(x)$ as $[x^n]f(x)$. You want$$[x^7](1-x^5)^4(1-x)^{-8}=[x^7](1-x)^{-8}-4[x^2](1-x)^{-8}.$$You can do the rest with the generalized binomial theorem.