

A306191


T(n,k) is a triangular array read by rows. Let S_n act on the set of size two subsets of {1,2,...,n}. T(n,k) is the number of permutations in S_n that fix exactly k size two subsets, n >= 1, 0 <= k <= binomial(n,2).


0



1, 0, 2, 2, 3, 0, 1, 14, 0, 9, 0, 0, 0, 1, 54, 40, 15, 0, 10, 0, 0, 0, 0, 0, 1, 304, 300, 0, 100, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 1, 2260, 1638, 630, 315, 0, 105, 70, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 18108, 12992, 5460, 1344, 1645, 0, 420, 0, 210, 0, 112, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
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OFFSET

1,3


COMMENTS

The action of S_n on the 2subsets of {1,2,...,n} is defined: For all pi in S_n, pi({i,j}) = {pi(i),pi(j)}.


LINKS



EXAMPLE

1,
0, 2,
2, 3, 0, 1,
14, 0, 9, 0, 0, 0, 1,
54, 40, 15, 0, 10, 0, 0, 0, 0, 0, 1,
304, 300, 0, 100, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 1,


MATHEMATICA

f[list_] := Flatten[Position[list /. x_ /; x > 0 > 1, 1]];
Level[CoefficientList[Table[n! PairGroupIndex[SymmetricGroup[n], s] /. {Table[s[i] > 1, {i, 2, Binomial[n, 2]}]}, {n, 1, 8}],
s[1]], {2}] // Grid


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



