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| rev | Admin | (Created page with "Prove that <math display="block"> u^{(2)}_{2n} = \frac 1{4^{2n}} \sum_{k = 0}^n \frac {(2n)!}{k!k!(n-k)!(n-k)!}\ , </math> and <math display="block"> u^{(3)}_{2n} = \frac 1{6^{2n}} \sum_{j,k} \frac {(2n)!}{j!j!k!k!(n-j-k)!(n-j-k)!}\ , </math> where the last sum extends over all non-negative <math>j</math> and <math>k</math> with <math>j+k \le n</math>. Also show that this last expression may be rewritten as <math display="block"> \frac 1{2^{2n}}{{2n}\choose n} \sum_{...") | Jun 15'24 at 2:40 | +543 |