A125699 Table, T(n,k) is the number of connected categories with n morphisms and k objects.

1, 2, 7, 1, 35, 6, 228, 28, 2, 2237, 159, 11, 31559, 1075, 77, 3, 1668997, 9389, 497, 24

Offset: 1

Author

Franklin T. Adams-Watters and Christian G. Bower, Jan 05 2007

Keywords

• tabf
• hard
• more
• nonn

Comments

Connected in the sense that if the morphism direction and composition is ignored, resulting in a multigraph, that multigraph is connected.

Examples

			The table starts:
        1;
        2;
        7,    1;
       35,    6;
      228,   28,   2;
     2237,  159,  11;
    31559, 1075,  77,  3;
  1668997, 9389, 497, 24;
  ...
		

Links

• Ben Spitz, SmallCategories
• Eric Weisstein's World of Mathematics, Category

Crossrefs

Cf. A125696, A125698 (row sums), A110654 (row lengths), A058129 (column 1), A125700 (diagonal sums), A125702 (T(2n-1, n)).

Extensions

a(14)-a(20) from Ben Spitz, Sep 02 2023