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 A379758 #33 Mar 10 2025 21:30:08
%S A379758 1,3,365,1323338487,1119556146543237253601352961,
%T A379758 3414445659328795239581367793706562556567987857578516541118092297328702035
%N A379758 Number of sequences in which the games of a fully symmetric single-elimination tournament with 2^n teams can be played if arbitrarily many arenas are available.
%C A379758 a(n) is also the number of tie-permitting labeled histories for a fully symmetric labeled topology with 2^n leaves.
%H A379758 Emily H. Dickey and Noah A. Rosenberg, <a href="https://doi.org/10.1098/rstb.2023.0307">Labelled histories with multifurcation and simultaneity</a>, Phil. Trans. R. Soc. B 380 (2025), 20230307. See Table 5.
%H A379758 Matthew C. King and Noah A. Rosenberg, <a href="https://doi.org/10.1080/0025570X.2023.2266389">A mathematical connection between single-elimination sports tournaments and evolutionary trees</a>, Math. Mag. 96 (2023), 484-497.
%F A379758 a(n) = Sum_{k=n..2^n-1} A380166(n,k).
%e A379758 For n=2 and a tournament with structure ((A,B),(C,D)), game (A,B) can be played before, after, or simultaneously with game (C,D), producing a(2)=3.
%Y A379758 Cf. A056972 (game sequences with only one arena).
%Y A379758 Row sums of A380166.
%K A379758 nonn
%O A379758 1,2
%A A379758 _Noah A Rosenberg_, Jan 01 2025