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A348071
Triangular array read by rows: T(n,k) is the number of undirected 2-regular labeled graphs whose smallest 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, 105, 0, 0, 0, 360, 0, 0, 672, 315, 0, 0, 0, 2520, 0, 0, 5320, 4536, 0, 0, 0, 0, 20160, 0, 0, 49500, 37800, 18144, 0, 0, 0, 0, 181440, 0, 0, 523215, 356400, 332640, 0, 0, 0, 0, 0, 1814400
OFFSET
1,10
COMMENTS
For the statistic "length of the largest component", see A348070.
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, 105, 0, 0, 0, 360;
0, 0, 672, 315, 0, 0, 0, 2520;
0, 0, 5320, 4536, 0, 0, 0, 0, 20160;
...
CROSSREFS
Row sums give A001205, n >= 1.
Right border gives A001710.
Columns 1 and 2 each give A000004.
Cf. A348070.
Sequence in context: A046775 A221787 A348070 * A204060 A359780 A085393
KEYWORD
nonn,tabl
AUTHOR
Steven Finch, Sep 27 2021
STATUS
approved