A079186 Number of non-anti-commutative closed binary operations on a set of order n.

0, 0, 8, 13851, 3530555392, 266023223876953125, 9644962193498535546171949056, 246832875573638552740275218239438131202951, 6127827569844832702316847785612357470342156990019367075840, 193794664362053647720926884692597177807303542565053791345764052714030485961865

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. A002489, A079187 (non-isomorphic), A079188, A079189, A079210.

Programs

PARI

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

Formula

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

a(n) = A002489(n) - A079189(n).

a(n) = Sum_{k>=1} A079178(n,k)*A079210(n,k).

Extensions

a(0)=0 prepended and terms a(5) and beyond from Andrew Howroyd, Jan 23 2022