

Title: Limit of a Combinatorial Sum Post by Michael Dagg on Aug 1^{st}, 2008, 11:51am Suppose G(m) = \sum_{i=1}^m \sum_{j=1}^m C(m,i) C(m,j) i^{mj} j^{mi} . Show that lim _{m>oo} [ (G(m))^{1/(2m)} ln m ]/m = 1/e . 

Title: Re: Limit of a Combinatorial Sum Post by Obob on Aug 1^{st}, 2008, 1:54pm Should that be j^{m1} or j^{mi}? 

Title: Re: Limit of a Combinatorial Sum Post by Michael Dagg on Aug 2^{nd}, 2008, 8:38pm Sorry, I made typo  j^{mi} is correct. Good observation, however, I hope no one spent any time on it  as written, the sum (whose terms are all positive) exceeds the term when i=j=m and that term is m^{m1} . 

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