A348071 -id:A348071 - cp's OEIS frontend

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.

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

Steven Finch, Sep 27 2021

For the statistic "length of the smallest component", see A348071.

			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;
...

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.

Row sums give A001205, n >= 1.
Right border gives A001710.
Columns 1 and 2 each give A000004.
Cf. A348071.

T(n,n) = A001710(n-1) for n >= 2.

cp's OEIS Frontend

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.

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