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 A260700 #47 Feb 22 2021 04:09:28
%S A260700 1,3,19,167,1791,22715,334031,5597524,105351108,2200768698,
%T A260700 50533675542,1265155704413,34300156146805,1001152439025205,
%U A260700 31301382564128969,1043692244938401836,36969440518414369896,1386377072447199902576,54872494774746771827248,2285943548113541477123970
%N A260700 Number of distinct parabolic double cosets of the symmetric group S_n.
%C A260700 This is closely related to the number of contingency tables on n elements (see A120733), but many contingency tables correspond to the same parabolic double coset, e.g., for n=2, there are 5 contingency tables, but only 3 distinct cosets.
%H A260700 Thomas Browning, <a href="/A260700/b260700.txt">Table of n, a(n) for n = 1..400</a>
%H A260700 Sara Billey, Matjaz Konvalinka, T. Kyle Petersen, William Slofstra, and Bridget Tenner, <a href="http://www.math.washington.edu/~billey/papers/DoubleCosets.pdf">Parabolic double cosets in Coxeter groups</a>, Discrete Mathematics and Theoretical Computer Science, Submitted, 2016.
%H A260700 Sara Billey, Matjaz Konvalinka, T. Kyle Petersen, William Slofstra, and Bridget Tenner, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p23">Parabolic double cosets in Coxeter groups</a>, Electron. J. Combin., Volume 25, Issue 1 (2018) P1.23.
%H A260700 Thomas Browning, <a href="https://arxiv.org/abs/2010.13256">Counting Parabolic Double Cosets in Symmetric Groups</a>, arXiv:2010.13256 [math.CO], 2020.
%H A260700 Masato Kobayashi, <a href="https://arxiv.org/abs/1907.11801">Construction of double coset system of a Coxeter group and its applications to Bruhat graphs</a>, arXiv:1907.11801 [math.CO], 2019.
%F A260700 a(n) is asymptotic to n! / (2^(log(2)/2 + 2) * log(2)^(2*n + 2)). [Conjectured _Vaclav Kotesovec_ Sep 08 2020, proved _Thomas Browning_ Oct 26 2020]
%e A260700 For n=2, there are three parabolic double cosets: {12}, {21}, and {12, 21}.
%Y A260700 Cf. A120733.
%K A260700 nonn
%O A260700 1,2
%A A260700 _Kyle Petersen_, Nov 16 2015
%E A260700 More terms from _Thomas Browning_, Sep 07 2020