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 A383885 #14 Jul 23 2025 16:08:23 %S A383885 0,0,1,9,118,4671,1199989,3661522792,105931872028455, %T A383885 24834563582168716305,53061406576514239124327751, %U A383885 2017720196187069550262596208732035,2756576827989210680367439732667802738773384,73919858836708511517426763179873538289329852786253510,29599937964452484359589007277447538854227891149791717673581110642 %N A383885 Number of nonisomorphic 3-nilpotent semigroups of order n. %C A383885 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 A383885 If r is the smallest such number, then S is said to have nilpotency degree r. %C A383885 This sequence counts semigroups S that have an element e such that for all x,y,z in S x*y*z = e. %C A383885 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 A383885 H. Jürgensen, F. Migliorini, and J. Szép, Semigroups. Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1991. %H A383885 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 A383885 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 A383885 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 A383885 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 A383885 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Se#semigroups">Index entries for sequences related to semigroups</a> %F A383885 a(n) = A383871(n)/n! * (1+o(1)). See Grillet paper in Links. %F A383885 For exact formula see the Distler and Mitchell paper. %Y A383885 Cf. A023814, A027851. %Y A383885 Cf. A383871, A383886. %K A383885 nonn %O A383885 1,4 %A A383885 _Elijah Beregovsky_, May 13 2025