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%I #17 Jan 27 2024 10:29:58
%S 1,0,1,0,2,0,3,3,0,3,18,0,4,97,11,0,4,655,194,0,5,7599,3469,44,0,5,
%T 169013,90529,1533,0,6,7554994,4108406,52986,179
%N Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with cooling number k = 1..(1+floor(n/2)).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CoolingNumber.html">Cooling Number</a>.
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, 2;
%e 0, 3, 3;
%e 0, 3, 18;
%e 0, 4, 97, 11;
%e 0, 4, 655, 194;
%e 0, 5, 7599, 3469, 44;
%e 0, 5, 169013, 90529, 1533;
%e 0, 6, 7554994, 4108406, 52986, 179;
%e ...
%Y Row sums are A001349.
%Y Cf. A369279 (counts for all simple graphs), A369278 (cooling number).
%K nonn,tabf,more
%O 1,5
%A _Eric W. Weisstein_, Jan 18 2024