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A384849 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with degeneracy k, 0 <= k < n.

%I A384849 #7 Jun 11 2025 17:51:54
%S A384849 1,1,1,1,2,1,1,5,4,1,1,9,18,5,1,1,19,85,43,7,1,1,36,471,442,85,8,1,1,
%T A384849 75,3378,6979,1758,144,10,1,1,152,31782,166258,70811,5421,231,11,1,1,
%U A384849 328,385205,5892753,5164116,547170,15239,342,13,1
%N A384849 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with degeneracy k, 0 <= k < n.
%H A384849 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphDegeneracy.html">Graph Degeneracy</a>.
%H A384849 Wikipedia, <a href="https://en.wikipedia.org/wiki/Degeneracy_(graph_theory)">Degeneracy (graph theory)</a>.
%F A384849 T(n,0) = T(n,n-1) = 1.
%F A384849 T(n,1) = A005195(n) - 1.
%e A384849 Triangle begins:
%e A384849   1;
%e A384849   1,   1;
%e A384849   1,   2,      1;
%e A384849   1,   5,      4,       1;
%e A384849   1,   9,     18,       5,       1;
%e A384849   1,  19,     85,      43,       7,      1;
%e A384849   1,  36,    471,     442,      85,      8,     1;
%e A384849   1,  75,   3378,    6979,    1758,    144,    10,   1;
%e A384849   1, 152,  31782,  166258,   70811,   5421,   231,  11,  1;
%e A384849   1, 328, 385205, 5892753, 5164116, 547170, 15239, 342, 13, 1;
%e A384849   ...
%Y A384849 Row sums are A000088.
%Y A384849 Cf. A005195, A352067 (connected case).
%K A384849 nonn,tabl
%O A384849 1,5
%A A384849 _Andrew Howroyd_, Jun 10 2025