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cellotim
Aug27-08, 03:54 PM
Does anyone have a compact formula (or any other kind of identity or formula for any related sum) for this sum:

\sum_{\sigma\in S_n} \prod_{i=0}^{n-1} (i + \sigma(i))!

where S_n is the set of permutations of S = \{0,\dots,n-1\} . It's similar to the formula for a determinant of the matrix A_{ij} = (i + j - 2)! but has no permutation signs.