What is the pattern in this summation expression?

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The discussion focuses on identifying the pattern in a summation expression involving a series. The expression includes terms like x - (2/6)x^3 - (20/120)x^5 and continues with coefficients 2, 20, 1080, and 140400. The user seeks to express this series in a general term format for summation from n = 1 to infinity. The goal is to find a consistent pattern for the coefficients to simplify the expression. Clarification is sought on how to derive the general term for these coefficients.
irony of truth
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I need some help

I got an expression involving series...

x - (2/6)x^3 - (20/120)x^5 - (1080/5040)x^7 - (140400/362880)x^9 - ...

I remove x from my summation expression.. but

Right now, I can express as a summation from n = 1 to infinity of

(??) x^(2n + 1) / (2n + 1)!

That is.. what is my pattern in this: 2, 20, 1080, 140400,... ?
 
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Am I correct to say that you want to find the general term to express it as one summation?
 
Yes. That is what I want to know... thank you for your clarification
 
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