This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118581 #8 Jun 16 2016 05:43:12
%S A118581 1,2,7,31,219,2134,30768,1658440,3685688857,105981863625149
%N A118581 Number of nonisomorphic semigroups of order <= n.
%C A118581 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.
%F A118581 a(n) = Sum_{i=0..n} A027851(i). a(n) = Sum_{i=0..n} (2*A001423(i) - A029851(i)).
%e A118581 a(7) = 1658440 = 1 + 1 + 5 + 24 + 188 + 1915 + 28634 + 1627672.
%Y A118581 Cf. A001329, A001423, A001426, A023814, A027851, A029851, A058108, A063756, A079173.
%K A118581 hard,nonn
%O A118581 0,2
%A A118581 _Jonathan Vos Post_, May 07 2006
%E A118581 a(8)-a(9) (using A027851) from _Giovanni Resta_, Jun 16 2016