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http://en.wikipedia.org/wiki/Permutation:
The number of permutations of n with k inversions is expressed by a Mahonian number,[12] it is the coefficient of Xk in the expansion of the product

which is also known (with q substituted for X) as the q-factorial [n]q! . The expansion of the product appears in Necklace (combinatorics).

http://oeis.org/A008302
A008302                Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_{i=0..n-1} (1+x+...+x^i), where k ranges from 0 to A000217(n-1).
        82

        1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 6, 5, 3, 1, 1, 4, 9, 15, 20, 22, 20, 15, 9, 4, 1, 1, 5, 14, 29, 49, 71, 90, 101, 101, 90, 71, 49, 29, 14, 5, 1, 1, 6, 20, 49, 98, 169, 259, 359, 455, 531, 573, 573, 531, 455, 359, 259, 169, 98, 49, 20, 6, 1

google À´µÄ, ´íÁ˲»Òª¹ÖÎÒ.
We_must_know. We_will_know.
7Â¥2013-12-31 03:15:50
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