A rational function is called positive if all its Taylor coefficients are positive.
  Friedrichs-Lewy conjecture states the positivity of the rational function
 \begin{eqnarray*}\frac{1}{
(1-x)(1- y)+(1- y)(1-z)+(1-z)(1-x)}
= \sum\limits_{ k,m,n\ge0}
a_{k,m, n }x^k y^mz^n.  \end{eqnarray*}
The conjecture was first proved by G. Szego. 

Let $P_n=\prod\limits_{i=1}^n(1-x_i)$, is it ture that the following rational function is positive \begin{eqnarray*}\frac{1}{
\sum\limits_{i=1}^n\frac{P_n}{1-x_i}}=\sum\limits_{i_1,i_2\cdots, i_n\ge 0}a_{i_1,i_2\cdots, i_n }x_1^{i_1}x_2^{i_2}\cdots x_n^{i_n}? \end{eqnarray*}

A reference http://129.81.170.14/~tamdeberhan/positivity.pdf ([Wayback Machine](http://web.archive.org/web/20170922235432/http://129.81.170.14/~tamdeberhan/positivity.pdf))