represent n! In any form other than the usual multiplication I.e. 1x2x3..n

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derive an equation to represent n! Instead of multiplying from 1 to n. One straight equation not involving factorial like the way we represent summation of r as n(n+1)/2, where r varies from 1 to n. A similar type of expression iam looking for

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There is no formula for $n!$ involving the usual arithmetic operations because $n!$ grows much faster than any rational function.