Tougher than the last two

Algebra Level 5

Find the coefficient of \(x^{40}\) in the expansion of the product below.

\[\large{\prod _{ n=1 }^{ 50 }{ \left( x+4n \right) } }\]

The length of the answer is nearly 35 digits so when you know the trick you may use a calculator and please post the solution.

Inspiration 1, inspiration 2


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