If n is a positive integer and ${C_k} = {\,^n}{C_k}$, then the value of ${\sum\limits_{k = 1}^n {{k^3}\left( {\frac{{{C_k}}}{{{C_{k - 1}}}}} \right)} ^2}$ =

  • A

    $\frac{{n(n + 1)(n + 2)}}{{12}}$

  • B

    $\frac{{n{{(n + 1)}^2}}}{{12}}$

  • C

    $\frac{{n{{(n + 2)}^2}(n + 1)}}{{12}}$

  • D

    None of these

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