

A228924


Irregular triangular array read by rows: T(n,k) is the number of derangement permutations of [n] that have exactly k inversions; n>=2, 1<=k<=binomial(n,2) for even n, 1<=k<=binomial(n,2)1 for odd n.


1



1, 0, 2, 0, 1, 4, 1, 2, 1, 0, 0, 4, 8, 4, 10, 10, 6, 2, 0, 0, 1, 12, 18, 16, 35, 44, 47, 40, 25, 14, 8, 4, 1, 0, 0, 0, 6, 32, 44, 60, 118, 160, 208, 244, 244, 214, 174, 140, 104, 64, 30, 10, 2, 0, 0, 0, 1, 24, 83, 118, 206, 388, 565, 802, 1068, 1308, 1466, 1508, 1479, 1414, 1290, 1076, 806, 544, 333, 186, 96, 46, 19, 6, 1
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OFFSET

2,3


COMMENTS

Row sums = A000166.
Sum_{k>=1} T(n,k)*k = A216239(n).
Sum_{even k} T(n,k) = A003221(n) and Sum_{odd k} T(n,k) = A000387(n).
It would be nice to have a closed formula for T(n,k).  Alois P. Heinz, Dec 31 2014


LINKS

Table of n, a(n) for n=2..82.


EXAMPLE

1;
0, 2;
0, 1, 4, 1, 2, 1;
0, 0, 4, 8, 4, 10, 10, 6, 2;
0, 0, 1, 12, 18, 16, 35, 44, 47, 40, 25, 14, 8, 4, 1;


MATHEMATICA

Map[Distribution[#, Range[1, Max[#]]]&, Table[Map[Inversions, Derangements[n]], {n, 2, 6}]]//Grid


CROSSREFS

Sequence in context: A182138 A258123 A121583 * A246862 A194686 A266213
Adjacent sequences: A228921 A228922 A228923 * A228925 A228926 A228927


KEYWORD

nonn,tabf


AUTHOR

Geoffrey Critzer, Sep 08 2013


STATUS

approved



