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On the Generating Function for Permutations with Repetitions and Inversions
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 101-102

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Let (a1, a2, ..., am), a i ∊ {l, 2, ..., n}, be an m-permutation of n (repetitions allowed) with exactly kj of the a's equal to j, j = 1, 2, ..., n, m = k 1+ ...+kn , fixed nonnegative integers. An inversion is a pair i, j such that i < j, ai > aj . Denote by N(r; k, ..., kn) the number of such permutations with exactly r inversions. 
Abramson, Morton. On the Generating Function for Permutations with Repetitions and Inversions. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 101-102. doi: 10.4153/CMB-1971-017-4
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     title = {On the {Generating} {Function} for {Permutations} with {Repetitions} and {Inversions}},
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     doi = {10.4153/CMB-1971-017-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-017-4/}
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