<s>[INST] find coefficient of $x^{50}$ Let $f(x)=\frac{1}{(1+x)(1+x^2)(1+x^4)}$then find the coefficient of term $x^{50}$ in $(f(x))^3$.I think that we can set $$(f(x))^3=\frac{a}{(1+x)^3}+\frac{b}{(1+x^2)^3}+\frac{c}{(1+x^4)^3}$$ and find a,b and c then use Taylor seri .
 [/INST] It won't work like that: $f(x)^3 = \dfrac{1}{(1+x)^3 (1+x^2)^3 (1+x^4)^3}$, and then the partial-fraction expansion will include terms in $1/(1+x)$, $1/(1+x)^2$, ...
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