

A125696


Number of categories with n morphisms.


5




OFFSET

0,3


LINKS

Table of n, a(n) for n=0..9.
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/(1x^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 2element monoid and a 1element monoid, and the category with 2 objects and a single morphism between the two objects,
* 1 category with 3 objects (3 separate 1element 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. AdamsWatters 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



