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 A360808 #20 Apr 05 2025 10:52:11
%S A360808 1,1,2,2,4,8,35,16,51,145,1112,1145,10929,41400,542785,40384,583169,
%T A360808 2781808,48558706,65461347,1277941540,7370563251,159694747220,
%U A360808 63387056365,1500631724572,10152855622657
%N A360808 Number of double cosets of the Sylow 2-subgroup of the symmetric group S_n.
%C A360808 Let S denote a Sylow 2-subgroup of the symmetric group S_n. Then a(n) is the number of double cosets SwS. [Corrected by _Benjamin Sambale_, Mar 08 2025]
%H A360808 Persi Diaconis, Eugenio Giannelli, Robert M. Guralnick, Stacey Law, Gabriel Navarro, Benjamin Sambale, and Hunter Spink, <a href="https://arxiv.org/abs/2504.01149">On the number and sizes of double cosets of Sylow subgroups of the symmetric group</a>, arXiv:2504.01149 [math.GR], 2025. See pp. 5, 15.
%F A360808 Define a symmetric function T_k recursively by T_0 = p_1 (power sum), and T_k is the plethysm h_2[T_{k-1}] for k>0. If n has the binary expansion 2^{a_0} + 2^{a_1} + ..., then set $U_n = T_{a_0}T_{a_1}... Then a_n = <U_n,U_n> (usual scalar product on symmetric functions).
%K A360808 nonn,more
%O A360808 1,3
%A A360808 _Richard Stanley_, Feb 21 2023
%E A360808 a(2) and a(5) corrected by _Benjamin Sambale_, Mar 08 2025