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 A371505 #28 May 22 2024 09:18:14 %S A371505 1,2,3,6,10,31,63,287,1099,8640,62658,1546891,29789119,2525655957 %N A371505 Number of sub-monoids of the monoid of uniform block permutations of size n that contain the symmetric group S_n. %C A371505 Also equal to the number of anti-chains in the poset of integer partitions of k not equal to (1^k) where mu < lambda iff mu is coarser than lambda and r(mu) >= r(lambda) where r(lambda) = smallest part of lambda not equal to 1. %H A371505 D. G. FitzGerald, <a href="https://doi.org/10.1017/S0004972700037692">A presentation for the monoid of uniform block permutations</a>, Bulletin of the Australian Mathematical Society, 68(2) (2003), 317--324. %H A371505 Rosa Orellana, Franco Saliola, Anne Schilling, and Mike Zabrocki, <a href="https://doi.org/10.5802/alco.243">Plethysm and the algebra of uniform block permutations</a>, Alg. Comb., Volume 5, no. 5 (2022), pp. 1165--1203. %H A371505 Rosa Orellana, Franco Saliola, Anne Schilling, and Mike Zabrocki, <a href="https://arxiv.org/abs/2405.09710">The lattice of submonoids of the uniform block permutations containing the symmetric group</a>, arXiv:2405.09710 [math.CO], 2024. See p. 3. %e A371505 a(3) = 3 because the uniform block permutations of size 3; S_3; and the monoid consisting of S_3 and the element with one block are the only three sub-monoids. %K A371505 nonn,more %O A371505 1,2 %A A371505 _Mike Zabrocki_, Apr 17 2024