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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.

%I A348071 #25 Nov 11 2021 10:25:11
%S A348071 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,
%T A348071 672,315,0,0,0,2520,0,0,5320,4536,0,0,0,0,20160,0,0,49500,37800,18144,
%U A348071 0,0,0,0,181440,0,0,523215,356400,332640,0,0,0,0,0,1814400
%N 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.
%C A348071 For the statistic "length of the largest component", see A348070.
%H A348071 Steven Finch, <a href="https://arxiv.org/abs/2111.05720">Permute, Graph, Map, Derange</a>, arXiv:2111.05720 [math.CO], 2021.
%H A348071 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 A348071 T(n,n) = A001710(n-1) for n >= 2.
%e A348071 Triangle begins:
%e A348071   0;
%e A348071   0,  0;
%e A348071   0,  0,    1;
%e A348071   0,  0,    0,    3;
%e A348071   0,  0,    0,    0,  12;
%e A348071   0,  0,   10,    0,   0,  60;
%e A348071   0,  0,  105,    0,   0,   0,  360;
%e A348071   0,  0,  672,  315,   0,   0,    0, 2520;
%e A348071   0,  0, 5320, 4536,   0,   0,    0,    0, 20160;
%e A348071 ...
%Y A348071 Row sums give A001205, n >= 1.
%Y A348071 Right border gives A001710.
%Y A348071 Columns 1 and 2 each give A000004.
%Y A348071 Cf. A348070.
%K A348071 nonn,tabl
%O A348071 1,10
%A A348071 _Steven Finch_, Sep 27 2021