The coefficient of $\frac{1}{x}$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is

  • A

    $\frac{{n!}}{{(n - 1)!(n + 1)!}}$

  • B

    $\frac{{(2n)\,!}}{{(n - 1)!(n + 1)!}}$

  • C

    $\frac{{n!}}{{(n - 1)!(n + 1)!}}$

  • D

    None of these

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