%I #17 Mar 11 2024 23:13:03

%S 1,0,1,0,2,0,6,0,19,2,0,83,29,0,500,353,0,4731,6386,0,75757,185323,0,

%T 2183854,9532714,3

%N Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with burning number k = 1..ceiling(sqrt(n)).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BurningNumber.html">Burning Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>.

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 2

%e 0, 6

%e 0, 19, 2;

%e 0, 83, 29;

%e 0, 500, 353;

%e 0, 4731, 6386;

%e 0, 75757, 185323;

%e 0, 2183854, 9532714, 3;

%e ...

%Y Row sums are A001349.

%Y Cf. A263322 (counts for all simple graphs), A369280 (cooling number).

%K nonn,tabf,more

%O 1,5

%A _Eric W. Weisstein_, Jan 18 2024