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A118581
Number of nonisomorphic semigroups of order <= n.
1
1, 2, 7, 31, 219, 2134, 30768, 1658440, 3685688857, 105981863625149
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.
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.
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