cp's OEIS Frontend

A023814 Number of associative binary operations on an n-set; number of labeled semigroups.

%I A023814 #30 Feb 16 2025 08:32:34
%S A023814 1,1,8,113,3492,183732,17061118,7743056064,148195347518186,
%T A023814 38447365355811944462
%N A023814 Number of associative binary operations on an n-set; number of labeled semigroups.
%H A023814 Alex Bailey, Martin Finn-Sell, and Robert Snocken, <a href="http://arxiv.org/abs/1409.2444">Subsemigroup, ideal and congruence growth of free semigroups</a>, arXiv preprint arXiv:1409.2444 [math.GR], 2014.
%H A023814 A. Distler and T. Kelsey, <a href="http://arxiv.org/abs/1301.6023">The semigroups of order 9 and their automorphism groups</a>, arXiv preprint arXiv:1301.6023 [math.CO], 2013.
%H A023814 C. Noebauer, <a href="http://www.algebra.uni-linz.ac.at/~noebsi/">Home page</a> [broken link]
%H A023814 C. Noebauer, <a href="ftp://www.algebra.uni-linz.ac.at/pub/noebauer/smallrings.ps.gz">The Numbers of Small Rings</a>
%H A023814 C. Noebauer, <a href="ftp://www.algebra.uni-linz.ac.at/pub/noebauer/thesis.ps.gz">Thesis on the enumeration of near-rings</a>
%H A023814 Eric Postpischil <a href="http://groups.google.com/groups?&amp;hl=en&amp;lr=&amp;ie=UTF-8&amp;selm=11802%40shlump.nac.dec.com&amp;rnum=2">Posting to sci.math newsgroup, May 21 1990</a>
%H A023814 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H A023814 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y A023814 Cf. A001423, A001426, A023813, A023815, A027851.
%Y A023814 a(n) + A079172(n) = A002489(n).
%K A023814 nonn,more
%O A023814 0,3
%A A023814 Lyle Ramshaw (ramshaw(AT)pa.dec.com)
%E A023814 a(8), a(9) from Distler and Kelsey (2013). - _N. J. A. Sloane_, Feb 19 2013