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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 16 19:22 EDT 2017. Contains 290626 sequences.