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 A332757 #27 Dec 18 2023 18:18:26
%S A332757 1,2,6,44,2064,4292864,18430828806144,339695459704759501186924544,
%T A332757 115393005344028056118476170527365821430429589033713664,
%U A332757 13315545682326887517994506072805639054664915214679444711916992466809542959290217586307654871548759705124864
%N A332757 Number of involutions (plus identity) in the n-fold iterated wreath product of C_2.
%C A332757 Also the number of involutions (plus identity) in a fixed Sylow 2-subgroup of the symmetric group of degree 2^n.
%C A332757 Also the number of involutory automorphisms (including identity) of the complete binary tree of height n.
%H A332757 Claudia Scheimbauer and Thomas Stempfhuber, <a href="https://arxiv.org/abs/2312.05051">Relative field theories via relative dualizability</a>, arXiv:2312.05051 [math.CT], 2023. See Theorem 6.7 at pages 5, 32, and 34.
%F A332757 a(n) = a(n-1)^2 + 2^(2^(n-1)-1), a(0) = 1.
%F A332757 a(n) ~ C^(2^n) for C = 1.611662639909645505576094683462403213269601342091954838587...
%e A332757 For n=2, the a(2)=6 elements satisfying x^2=1 in C_2 wr C_2 (which is isomorphic to the dihedral group of degree 4) are the identity and (13), (24), (12)(34), (13)(24), (14)(23).
%t A332757 Nest[Append[#1, #1[[-1]]^2 + 2^(2^(#2 - 1) - 1)] & @@ {#, Length@ #} &, {1}, 9] (* _Michael De Vlieger_, Feb 25 2020 *)
%Y A332757 Cf. A332758.
%K A332757 nonn
%O A332757 0,2
%A A332757 _Nick Krempel_, Feb 22 2020