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Irregular triangle read by rows: distribution of inversion numbers over the set of permutations of the multiset {1,1,2,2,3,3,...,n,n} avoiding the pattern 123.
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%I #10 Jul 27 2017 11:11:03

%S 1,1,1,2,1,1,0,0,0,0,3,3,6,7,9,7,5,2,1,0,0,0,0,0,0,0,0,1,1,4,6,15,18,

%T 28,35,44,47,49,42,31,18,9,3,1

%N Irregular triangle read by rows: distribution of inversion numbers over the set of permutations of the multiset {1,1,2,2,3,3,...,n,n} avoiding the pattern 123.

%H A. M. Baxter, <a href="https://pdfs.semanticscholar.org/2c5d/79e361d3aecb25c380402144177ad7cd9dc8.pdf">Algorithms for Permutation Statistics</a>, Ph. D. Dissertation, Rutgers University, May 2011. See Table 4.1.

%e Triangle begins:

%e 1,

%e 1,1,2,1,1,

%e 0,0,0,0,3,3,6,7,9,7,5,2,1,

%e 0,0,0,0,0,0,0,0,1,1,4,6,15,18,28,35,44,47,49,42,31,18,9,3,1,

%e ...

%Y Row sums give A220097.

%K nonn,tabf,more

%O 1,4

%A _N. J. A. Sloane_, Jun 24 2017