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The coefficient of $x^{20}$ in the expansion of ${(1 + \frac{1}{1!} x + \frac{1}{2!} x^{2} + \dots + \frac{1}{20!} x^{20})}^{3}$ is

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Correct option is C

Note that, coefficient of x20 in1+11!x+12!x2+…+120!x203 = coefficient of x20 in1+11!x+12!x2+…+120!x20+121!x21+…3 = coefficient of x20in e3x=32020!

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The coefficient of x20 in the expansion of 1+11!x+12!x2+…+120!x203is

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The coefficient of $x^{20}$ in the expansion of ${(1 + \frac{1}{1!} x + \frac{1}{2!} x^{2} + \dots + \frac{1}{20!} x^{20})}^{3}$ is