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 A332758 #24 Apr 09 2025 14:14:51
%S A332758 0,1,3,17,417,206657,44854599297,2021158450131287670017,
%T A332758 4085251621720569336520310526902208564886017,
%U A332758 16689280870666586360302304039420036318743515355074220606298783584912362351240766944257
%N A332758 Number of fixed-point free involutions in the n-fold iterated wreath product of C_2.
%C A332758 Also the number of fixed-point free involutions in a fixed Sylow 2-subgroup of the symmetric group of degree 2^n.
%C A332758 Also the number of fixed-point free involutory automorphisms of the complete binary tree of height n.
%F A332758 a(n) = a(n-1)^2 + 2^(2^(n-1)-1), a(0) = 0.
%F A332758 a(n) ~ C^(2^n) for C = 1.467067423065535412629251121186749718727038915553188083467...
%F A332758 a(n) = 2^(2^(n-1)) * b(n), where b(0) = 0, b(n+1) = b(n)^2 + 1/2. - _Jianing Song_, Apr 09 2025
%e A332758 For n=2, the a(2)=3 fixed-point free involutions in C_2 wr C_2 (which is isomorphic to the dihedral group of degree 4) are (12)(34), (13)(24), and (14)(23).
%t A332758 Nest[Append[#1, #1[[-1]]^2 + 2^(2^(#2 - 1) - 1)] & @@ {#, Length@ #} &, {0}, 9] (* _Michael De Vlieger_, Feb 25 2020 *)
%Y A332758 Cf. A332757.
%K A332758 nonn
%O A332758 0,3
%A A332758 _Nick Krempel_, Feb 22 2020