A023815 Number of binary operations on an n-set that are commutative and associative; labeled commutative semigroups.

1, 1, 6, 63, 1140, 30730, 1185072, 66363206, 7150843144, 3829117403448

Offset: 0

Author

Lyle Ramshaw (ramshaw(AT)pa.dec.com)

Keywords

• nonn
• hard
• more

Links

• Eric Postpischil Posting to sci.math newsgroup, May 21 1990
• Amit Sehgal, Sunil Kumar, Sarita, Yashpal, Commutative Associative Binary Operations on a Set with Five Elements, J. Phys.: Conf. Ser. (2018) 1000 012063
• Eric Weisstein's World of Mathematics, Semigroup.
• Index entries for sequences related to semigroups

Crossrefs

Row sums of A058167.

Cf. A001423, A001426 (isomorphism classes), A023813 (commutative only), A023814 (associative only), A027851.

Cf. A002489, A079192, A079195, A079198, A079201, A079210.

Formula

a(n) + A079192(n) + A079195(n) + A079198(n) = A002489(n).

a(n) = Sum_{k>=1} A079201(n,k)*A079210(n,k). - Andrew Howroyd, Jan 26 2022

Extensions

a(8) from Andrew Howroyd, Jan 26 2022

a(9) from Andrew Howroyd, Feb 14 2022