A228924 - OEIS

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, 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

Alois P. Heinz, Rows n = 2..23, flattened

EXAMPLE

Triangle T(n,k) begins: