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A360880 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) multigraphs with n edges and k nodes, loops allowed, n >= 1, 2 <= k <= n + 1.

%I A360880 #7 Feb 25 2023 20:58:03
%S A360880 1,2,0,4,1,0,6,2,1,0,9,6,3,1,0,12,14,13,4,1,0,16,28,39,22,5,1,0,20,52,
%T A360880 112,98,39,6,1,0,25,93,281,383,236,63,8,1,0,30,152,655,1304,1220,515,
%U A360880 102,9,1,0,36,242,1408,3980,5418,3512,1077,153,11,1,0
%N A360880 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) multigraphs with n edges and k nodes, loops allowed, n >= 1, 2 <= k <= n + 1.
%H A360880 Andrew Howroyd, <a href="/A360880/b360880.txt">Table of n, a(n) for n = 1..190</a> (rows 1..19)
%e A360880 Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
%e A360880    1;
%e A360880    2,   0;
%e A360880    4,   1,   0;
%e A360880    6,   2,   1,    0;
%e A360880    9,   6,   3,    1,    0;
%e A360880   12,  14,  13,    4,    1,   0;
%e A360880   16,  28,  39,   22,    5,   1,   0;
%e A360880   20,  52, 112,   98,   39,   6,   1, 0;
%e A360880   25,  93, 281,  383,  236,  63,   8, 1, 0;
%e A360880   30, 152, 655, 1304, 1220, 515, 102, 9, 1, 0;
%e A360880   ...
%Y A360880 Columns k=2..3 are A002620(n+1), A050531(n-3).
%Y A360880 Row sums are A360881.
%Y A360880 Cf. A290428, A322115, A339070, A339160, A360870.
%K A360880 nonn,tabl
%O A360880 1,2
%A A360880 _Andrew Howroyd_, Feb 25 2023