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.

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

Table of n, a(n) for n=1..66.

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

Adjacent sequences: A348068 A348069 A348070 * A348072 A348073 A348074

Keyword

nonn,tabl

Author

Steven Finch, Sep 27 2021

Status

approved