|
%I #21 Jan 26 2019 12:07:41
%S 1,1,3,11,55,329,2858,36440,1723286,3687822810
%N Number of categories with n morphisms.
%H Geoff Cruttwell, <a href="https://www.mta.ca/uploadedFiles/Community/Bios/Geoff_Cruttwell/ams2014CruttwellCountingFiniteCats.pdf">Counting Finite Categories</a>, presentation, (2018).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Category.html">Category</a>
%F Euler transform of A125698.
%F G.f.: Product_{i>=1} 1/(1-x^i)^A125698(i).
%e The 11 categories with 3 morphisms consist of:
%e * 7=A058129(3) categories with 1 object (monoids),
%e * 3 categories with 2 objects, consisting of: 2=A058129(2) disconnected combinations of a 2-element monoid and a 1-element monoid, and the category with 2 objects and a single morphism between the two objects,
%e * 1 category with 3 objects (3 separate 1-element monoids).
%Y Cf. A058129, A125697, A125698, A125720.
%K hard,more,nonn
%O 0,3
%A _Franklin T. Adams-Watters_ and _Christian G. Bower_, Jan 05 2007
%E a(0) and a(7)-a(9) from _Thomas Anton_, from the work of G. Cruttwell and R. Leblanc, Jan 25 2019
| 