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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

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: A094259 A091845 A020061 * 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 October 14 00:07 EDT 2019. Contains 327990 sequences. (Running on oeis4.)