I'm having problems with finding the combinatorial interpretation of this sum: $$\sum_{i,j} i \cdot j \cdot \binom{2n}{i}\cdot \binom{2n}{j} \cdot \binom{2n}{3n-i-j}$$

Can anyone help, please?

  • $\begingroup$ maybe the Sigma sign is the problem? it's $\sum_{i=0}^{n} \sum_{j=0}^{n}$. $\endgroup$ – Alex Jun 13 '14 at 15:00
  • 2
    $\begingroup$ Are you sure that the last binomial term has $3n-i-j$ and not $2n-i-j$? $\endgroup$ – Anurag A Jun 13 '14 at 15:46

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