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

0,3

Links

Table of n, a(n) for n=0..9.

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

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

Crossrefs

Row sums of A058167.

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

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

Sequence in context: A271607 A360481 A079244 * A249590 A034665 A339140

Adjacent sequences: A023812 A023813 A023814 * A023816 A023817 A023818

Keyword

nonn,hard,more

Author

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

Extensions

a(8) from Andrew Howroyd, Jan 26 2022

a(9) from Andrew Howroyd, Feb 14 2022

Status

approved