A118581 Number of nonisomorphic semigroups of order <= n.

1, 2, 7, 31, 219, 2134, 30768, 1658440, 3685688857, 105981863625149

Offset: 0

Author

Jonathan Vos Post, May 07 2006

Keywords

• hard
• nonn

Comments

Semigroup analog of A063756 Number of groups of order <= n. a semigroup is an algebraic structure consisting of a set S closed under an associative binary operation (and thus is an associative groupoid). Some sources require that a semigroup have an identity element (in which case semigroups are identical to monoids). Not all sources agree that S should be nonempty. This sequence assumes that a semigroup may be empty and need not have an identity.

Examples

			a(7) = 1658440 = 1 + 1 + 5 + 24 + 188 + 1915 + 28634 + 1627672.
		

Crossrefs

Cf. A001329, A001423, A001426, A023814, A027851, A029851, A058108, A063756, A079173.

Formula

a(n) = Sum_{i=0..n} A027851(i). a(n) = Sum_{i=0..n} (2*A001423(i) - A029851(i)).

Extensions

a(8)-a(9) (using A027851) from Giovanni Resta, Jun 16 2016