A348070 - OEIS

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.

%I #24 Nov 11 2021 10:24:58

%S 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,

%T 315,672,0,0,2520,0,0,280,0,4536,5040,0,0,20160,0,0,0,6300,18144,

%U 37800,43200,0,0,181440,0,0,0,51975,55440,332640,356400,415800,0,0,1814400

%N 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.

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

%H Steven Finch, <a href="https://arxiv.org/abs/2111.05720">Permute, Graph, Map, Derange</a>, arXiv:2111.05720 [math.CO], 2021.

%H D. Panario and B. Richmond, <a href="https://doi.org/10.1007/s00453-001-0047-1">Exact largest and smallest size of components</a>, Algorithmica, 31 (2001), 413-432.

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

%e Triangle begins:

%e 0;

%e 0, 0;

%e 0, 0, 1;

%e 0, 0, 0, 3;

%e 0, 0, 0, 0, 12;

%e 0, 0, 10, 0, 0, 60;

%e 0, 0, 0, 105, 0, 0, 360;

%e 0, 0, 0, 315, 672, 0, 0, 2520;

%e 0, 0, 280, 0, 4536, 5040, 0, 0, 20160;

%e ...

%Y Row sums give A001205, n >= 1.

%Y Right border gives A001710.

%Y Columns 1 and 2 each give A000004.

%Y Cf. A348071.

%K nonn,tabl

%O 1,10

%A _Steven Finch_, Sep 27 2021