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 A225797 #29 May 23 2016 17:04:39 %S A225797 2,12,114,1512,25826,541254,13479500,389855014,12870896154, %T A225797 478623817564,19835696733562,908279560428462,45625913238986060, %U A225797 2499342642591607902,148545280714724993650,9537237096314268691724 %N A225797 The number of idempotents in the partition monoid on [1..n]. %C A225797 The partition monoid is the set of partitions on [1..2n] and multiplication as defined in Halverson and Ram. %C A225797 No general formula is known for the number of idempotents in the partition monoid. %C A225797 a(2) to a(8) were first produced using the Semigroups package for GAP, which contains code based on earlier calculations by Max Neunhoeffer. %H A225797 James Mitchell, <a href="/A225797/b225797.txt">Table of n, a(n) for n = 1..115</a> %H A225797 I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., <a href="http://arxiv.org/abs/1408.2021">Enumeration of idempotents in diagram semigroups and algebras</a>, arXiv preprint arXiv:1408.2021 [math.GR], 2014. %H A225797 T. Halverson, A. Ram, <a href="http://dx.doi.org/10.1016/j.ejc.2004.06.005">Partition algebras</a>, European J. Combin. 26 (6) (2005) 869-921. %H A225797 J. D. Mitchell et al., <a href="https://gap-packages.github.io/Semigroups/">Semigroups</a> package for GAP. %o A225797 (GAP) for i in [2 .. 8] do %o A225797 Print(NrIdempotents(PartitionMonoid(i)), "\n"); %o A225797 od; %Y A225797 Cf. A227545. %K A225797 nonn %O A225797 1,1 %A A225797 _James Mitchell_, Jul 27 2013 %E A225797 a(9)-a(12) from _James East_, Feb 07 2014 %E A225797 a(13) onwards from _James Mitchell_, May 23 2016