We have an $n$ natural number. Prove, that $2(3n)!$ is divisible with $n!(n+1)!(n+2)!.$

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We have an $n$ natural number. Prove, that $2(3n)!$ is divisible with $n!(n+1)!(n+2)!.$

I tried to make it look simplier, but can't prove that this is true.

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Hint: Use the Legendre's formula.