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A332401 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with domination number k, n >= 1, 1 <= k <= A065033(n+1).

%I A332401 #12 Feb 16 2025 08:33:59
%S A332401 1,1,2,4,2,11,10,34,76,2,156,655,42,1044,9162,905,6,12346,219823,
%T A332401 28720,191,274668,9864065,1568173,9644,21
%N A332401 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with domination number k, n >= 1, 1 <= k <= A065033(n+1).
%C A332401 Bivariate inverse Euler transform of A263284. This sequence can be derived from A263284 because the domination number of a disconnected graph is the sum of the domination numbers of its components.
%C A332401 Connected graphs with greatest domination number include the path graph.
%H A332401 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>
%H A332401 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dominating_set">Dominating set</a>
%e A332401 Triangle begins:
%e A332401       1;
%e A332401       1;
%e A332401       2;
%e A332401       4,      2;
%e A332401      11,     10;
%e A332401      34,     76,     2;
%e A332401     156,    655,    42;
%e A332401    1044,   9162,   905,   6;
%e A332401   12346, 219823, 28720, 191;
%e A332401    ....
%Y A332401 Row sums are A001349.
%Y A332401 Column k=1 is A000088(n-1).
%Y A332401 Cf. A065033, A263284, A286958.
%K A332401 nonn,tabf,more
%O A332401 1,3
%A A332401 _Andrew Howroyd_, Feb 11 2020