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\end{equation}  evaluating this function gives something that looks like $1/x$, however, after diagnosing the coefficients of the Laurent series, we find \begin{equation}  f(x)=\frac{1}{x}-\frac{2}{x^3}+\frac{10}{x^5}-\frac{74}{x^7}+\frac{706}{x^9}-\cdots  \end{equation} a search on OEIS gives sequence A000698 which we believe to be plausible.