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Calculus Level 5

\[\prod _{ x=1 }^{ \infty }{ \frac { { x }^{ 2 }\left( 16{ x }^{ 4 }+24{ x }^{ 2 }+9 \right) }{ 16\left( { x }^{ 6 }+2{ x }^{ 3 }+1 \right) } }\]

The following infinite product can be expressed in the form \[\frac { A }{ B } \tanh ^{ 2 }{ \left( \frac { \sqrt { B } }{ C } \pi \right) }\] with \({ A }\) a perfect square and \({ B }\) and \({ C }\) prime numbers. Find \(A\times B\times C\).

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