A079189 Number of anti-commutative closed binary operations (groupoids) on a set of order n.

1, 1, 8, 5832, 764411904, 32000000000000000, 669462604992000000000000000, 10090701947420325348336258984797490118656, 149274165541848061518941637595308945760198454444667437056, 2832386113499265897149023834314938475799908379160975581551362823935905234944

Offset: 0

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..20
• C. van den Bosch, Closed binary operations on small sets
• Index entries for sequences related to groupoids

Crossrefs

Cf. A023813, A079186, A079190 (isomorphism classes), A079191, A079210.

Programs

PARI

a(n) = (n^n)*((n^2-n)^((n^2-n)/2)) \\ Andrew Howroyd, Jan 23 2022

Formula

a(n) = (n^n)*((n^2-n)^((n^2-n)/2)).

a(n) = A002489(n) - A079186(n).

a(n) = Sum_{k>=1} A079191(n,k)*A079210(n,k).

a(n) = A023813(n)*A023813(n-1).

Extensions

Edited and extended by Christian G. Bower, Dec 12 2003

a(0)=1 prepended, a(8) corrected and a(9) added by Andrew Howroyd, Jan 23 2022