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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 A348070 #24 Nov 11 2021 10:24:58
%S A348070 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 A348070 315,672,0,0,2520,0,0,280,0,4536,5040,0,0,20160,0,0,0,6300,18144,
%U A348070 37800,43200,0,0,181440,0,0,0,51975,55440,332640,356400,415800,0,0,1814400
%N 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.
%C A348070 For the statistic "length of the smallest component", see A348071.
%H A348070 Steven Finch, <a href="https://arxiv.org/abs/2111.05720">Permute, Graph, Map, Derange</a>, arXiv:2111.05720 [math.CO], 2021.
%H A348070 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 A348070 T(n,n) = A001710(n-1) for n >= 2.
%e A348070 Triangle begins:
%e A348070   0;
%e A348070   0,  0;
%e A348070   0,  0,   1;
%e A348070   0,  0,   0,   3;
%e A348070   0,  0,   0,   0,   12;
%e A348070   0,  0,  10,   0,    0,   60;
%e A348070   0,  0,   0, 105,    0,    0,  360;
%e A348070   0,  0,   0, 315,  672,    0,    0, 2520;
%e A348070   0,  0, 280,   0, 4536, 5040,    0,    0, 20160;
%e A348070 ...
%Y A348070 Row sums give A001205, n >= 1.
%Y A348070 Right border gives A001710.
%Y A348070 Columns 1 and 2 each give A000004.
%Y A348070 Cf. A348071.
%K A348070 nonn,tabl
%O A348070 1,10
%A A348070 _Steven Finch_, Sep 27 2021