What's the Exclamation Mark for?

Algebra Level 4

\[\Large \frac {\color{green}3!}{\color{violet}1!} + \frac{\color{green}4!}{\color{violet}2!} + \frac{\color{green}5!}{\color{violet}3!} + \dots + \frac {\color{green}{50}!}{\color{violet}{48}!} = \ \color{blue}? \]

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