Fiery Factorials!

1!×2!×3!××10!(1!)2(3!)2(5!)2(7!)2(9!)2=15×2n \large \dfrac{1! \times2!\times 3!\times \cdots \times 10!}{(1!)^2(3!)^2(5!)^2(7!)^2(9!)^2}=15\times2^n

What is the value of nn such that it satisfy the equation above?

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