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 A125696 Number of categories with n morphisms. 5
 1, 1, 3, 11, 55, 329, 2858, 36440, 1723286, 3687822810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Geoff Cruttwell, Counting Finite Categories, presentation, (2018). Eric Weisstein's World of Mathematics, Category FORMULA Euler transform of A125698. G.f.: Product_{i>=1} 1/(1-x^i)^A125698(i). EXAMPLE The 11 categories with 3 morphisms consist of: * 7=A058129(3) categories with 1 object (monoids), * 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, * 1 category with 3 objects (3 separate 1-element monoids). CROSSREFS Cf. A058129, A125697, A125698, A125720. Sequence in context: A091845 A020061 A330041 * A001776 A261001 A207556 Adjacent sequences:  A125693 A125694 A125695 * A125697 A125698 A125699 KEYWORD hard,more,nonn AUTHOR Franklin T. Adams-Watters and Christian G. Bower, Jan 05 2007 EXTENSIONS a(0) and a(7)-a(9) from Thomas Anton, from the work of G. Cruttwell and R. Leblanc, Jan 25 2019 STATUS approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)