A090602 Number of n-element labeled groupoids with an identity.

0, 1, 4, 243, 1048576, 762939453125, 170581728179578208256, 18562115921017574302453163671207, 1427247692705959881058285969449495136382746624, 106111661199647248543687855752712667991103904330482569981872649

Offset: 0

Author

Christian G. Bower, Dec 05 2003

Keywords

• nonn

Comments

Also labeled groupoids with an absorbant (zero) element.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..20
• Eric Postpischil Posting to sci.math newsgroup, May 21 1990
• Eric Weisstein's World of Mathematics, Groupoid
• Wikipedia, Magma (algebra)
• Index entries for sequences related to groupoids

Crossrefs

Cf. A090601 (isomorphism classes), A090603.

Programs

PARI

a(n) = n^((n-1)^2+1) \\ Andrew Howroyd, Jan 23 2022

Formula

a(n) = n^((n-1)^2+1).

a(n) = A090603(n)*n.

Extensions

a(0)=0 prepended and a(9) added by Andrew Howroyd, Jan 23 2022