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).

1, 1, 2, 4, 2, 11, 10, 34, 76, 2, 156, 655, 42, 1044, 9162, 905, 6, 12346, 219823, 28720, 191, 274668, 9864065, 1568173, 9644, 21

Offset: 1

Author

Andrew Howroyd, Feb 11 2020

Keywords

• nonn
• tabf
• more

Comments

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.

Connected graphs with greatest domination number include the path graph.

Examples

			Triangle begins:
      1;
      1;
      2;
      4,      2;
     11,     10;
     34,     76,     2;
    156,    655,    42;
   1044,   9162,   905,   6;
  12346, 219823, 28720, 191;
   ....
		

Links

• Eric Weisstein's World of Mathematics, Domination Number
• Wikipedia, Dominating set

Crossrefs

Row sums are A001349.

Column k=1 is A000088(n-1).

Cf. A065033, A263284, A286958.