A125696 Number of categories with n morphisms.

1, 1, 3, 11, 55, 329, 2858, 36440, 1723286, 3687822810

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/(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: A020061 A370514 A330041 * A001776 A261001 A207556

Adjacent sequences: A125693 A125694 A125695 * A125697 A125698 A125699

Keyword

hard,more,nonn,changed

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