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Question Number 156485 by MathSh last updated on 11/Oct/21

$$2021!\underset{\mathbf{n}=0}{\sum ^{\mathrm{\infty }}}\underset{\mathbf{k}=0}{\sum ^{\mathrm{\infty }}}\frac{1}{\underset{\mathbf{m}=1}{\prod ^{2022}}(\mathrm{n}+\mathrm{k}+\mathrm{m})}=\frac{1}{\mathrm{A}}$$$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathbf{A}$$

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