Can you help me understand the beautiful formula for multifactorials?

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The discussion centers on the formula for multifactorials, specifically addressing the expression for m(n) as defined in the MathWorld article. The formula is articulated as m(n) = 1/(n!) + 1/(n! * (n-1)!) + 1/(n! * (n-1)! * (n-2)!) + ... The user questions the accuracy of the formula, suggesting that the summation should start with k=0 instead of n=0. The conversation highlights the relationship between multifactorials and the number of exclamation marks used in notation, such as doublefactorials.

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a1call
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I think there's a mistake in the MathWorld formula the summation of n=0 should be k=0

##m(n) = 1/( n! ) + 1/( n! * (n-1)! ) + 1/( n! * (n-1)! * (n-2)! ) + ...##
 
Thank you for your reply jedishrfu,
The article seems related to multifactorials with k being the number of exclamation marks, such as 2 marks for doublefactorial and more by similar extension.
 

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