A125699 - OEIS

%I #14 Feb 16 2025 08:33:04

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

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

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

%H Ben Spitz, <a href="https://github.com/diracdeltafunk/SmallCategories#statistics">SmallCategories</a>

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

%e The table starts:

%e         1;

%e         2;

%e         7,    1;

%e        35,    6;

%e       228,   28,   2;

%e      2237,  159,  11;

%e     31559, 1075,  77,  3;

%e   1668997, 9389, 497, 24;

%e   ...

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

%K tabf,hard,more,nonn,changed

%O 1,2

%A _Franklin T. Adams-Watters_ and _Christian G. Bower_, Jan 05 2007

%E a(14)-a(20) from _Ben Spitz_, Sep 02 2023