Differences in Squares (with factorials)

The double factorial of a positive integer is defined by:

\(n!! = \begin{cases} 1 \cdot 3 \cdot 5 \cdots (n-2) \cdot n, & \text{if }n \equiv 1 \pmod{2} \\ 2 \cdot 4 \cdot 6 \cdots (n-2) \cdot n, & \text{if }n \equiv 0 \pmod{2} \end{cases}\)

Find the number of ways the value of \(\dfrac{2014!}{2012!!}\) can be expressed as \(a^2-b^2\), where \(a\) and \(b\) are positive integers and \(a>b\).

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