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 A383886 #7 May 14 2025 01:16:42 %S A383886 0,0,1,8,84,2660,609797,1831687022,52966239062973, %T A383886 12417282095522918811,26530703289252298687053072, %U A383886 1008860098093547692911901804990610,1378288413994605341053354105969660808031163,36959929418354255758713676933402538920157765946956889,14799968982226242179794503639146983952853044950740907666303436922 %N A383886 Number of 3-nilpotent semigroups, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator). %C A383886 A semigroup S is nilpotent if there exists a natural number r such that the set S^r of all products of r elements of S has size 1. %C A383886 If r is the smallest such number, then S is said to have nilpotency degree r. %C A383886 This sequence counts semigroups S that have an element e such that for all x,y,z in S x*y*z = e. %C A383886 In 1976 Kleitman, Rothschild and Spencer gave an argument asserting that the proportion of 3-nilpotent semigroups, amongst all semigroups of order n, is asymptotically 1. Later opinion regards their argument as incomplete, and no satisfactory proof has been found. %D A383886 H. Jürgensen, F. Migliorini, and J. Szép, Semigroups. Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1991. %H A383886 Andreas Distler and James D. Mitchell, <a href="https://doi.org/10.48550/arXiv.1201.3529">The number of nilpotent semigroups of degree 3</a>, arXiv:1201.3529 [math.CO], 2012. %H A383886 Igor Dolinka, D. G. FitzGerald, and James D. Mitchell, <a href="https://doi.org/10.48550/arXiv.2411.00466">Semirigidity and the enumeration of nilpotent semigroups of index three</a>, arXiv:2411.00466 [math.CO], 2024. %H A383886 Pierre A. Grillet, <a href="https://doi.org/10.1080/00927872.2013.790036">Counting Semigroups</a>, Communications in Algebra, 43(2), 574-596, (2014). %H A383886 D. J. Kleitman, B. R. Rothschild, and J. H. Spencer, <a href="https://doi.org/10.2307/2041879">The number of semigroups of order n</a>, Proc. Amer. Math. Soc. 55 (1976), 227-232. %H A383886 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Se#semigroups">Index entries for sequences related to semigroups</a> %F A383886 a(n) = A383871(n)/2n! * (1+o(1)). See Grillet paper in Links. %Y A383886 Cf. A023814, A001423. %Y A383886 Cf. A383885, A383871. %K A383886 nonn %O A383886 1,4 %A A383886 _Elijah Beregovsky_, May 13 2025