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Sum of series factorial(n)^2/factorial(k^n)



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The solution

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  oo       
____       
\   `      
 \       2 
  \    n!  
   )  -----
  /   / n\ 
 /    \k /!
/___,      
n = 1      
$$\sum_{n=1}^{\infty} \frac{n!^{2}}{\left(k^{n}\right)!}$$
Sum(factorial(n)^2/factorial(k^n), (n, 1, oo))
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