

A118581


Number of nonisomorphic semigroups of order <= n.


1




OFFSET

0,2


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.


LINKS

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


FORMULA

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


EXAMPLE

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


CROSSREFS

Cf. A001329, A001423, A001426, A023814, A027851, A029851, A058108, A063756, A079173.
Sequence in context: A306037 A046907 A091312 * A102159 A309164 A102163
Adjacent sequences: A118578 A118579 A118580 * A118582 A118583 A118584


KEYWORD

hard,nonn


AUTHOR

Jonathan Vos Post, May 07 2006


EXTENSIONS

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


STATUS

approved



