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A348070
Triangular array read by rows: T(n,k) is the number of undirected 2-regular labeled graphs whose largest connected component has exactly k nodes; n >= 1, 1 <= k <= n.
1
0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 12, 0, 0, 10, 0, 0, 60, 0, 0, 0, 105, 0, 0, 360, 0, 0, 0, 315, 672, 0, 0, 2520, 0, 0, 280, 0, 4536, 5040, 0, 0, 20160, 0, 0, 0, 6300, 18144, 37800, 43200, 0, 0, 181440, 0, 0, 0, 51975, 55440, 332640, 356400, 415800, 0, 0, 1814400
OFFSET
1,10
COMMENTS
For the statistic "length of the smallest component", see A348071.
LINKS
Steven Finch, Permute, Graph, Map, Derange, arXiv:2111.05720 [math.CO], 2021.
D. Panario and B. Richmond, Exact largest and smallest size of components, Algorithmica, 31 (2001), 413-432.
FORMULA
T(n,n) = A001710(n-1) for n >= 2.
EXAMPLE
Triangle begins:
0;
0, 0;
0, 0, 1;
0, 0, 0, 3;
0, 0, 0, 0, 12;
0, 0, 10, 0, 0, 60;
0, 0, 0, 105, 0, 0, 360;
0, 0, 0, 315, 672, 0, 0, 2520;
0, 0, 280, 0, 4536, 5040, 0, 0, 20160;
...
CROSSREFS
Row sums give A001205, n >= 1.
Right border gives A001710.
Columns 1 and 2 each give A000004.
Cf. A348071.
Sequence in context: A108707 A046775 A221787 * A348071 A204060 A359780
KEYWORD
nonn,tabl
AUTHOR
Steven Finch, Sep 27 2021
STATUS
approved