A332758 Number of fixed-point free involutions in the n-fold iterated wreath product of C_2.

0, 1, 3, 17, 417, 206657, 44854599297, 2021158450131287670017, 4085251621720569336520310526902208564886017, 16689280870666586360302304039420036318743515355074220606298783584912362351240766944257

Offset

0,3

Comments

Also the number of fixed-point free involutions in a fixed Sylow 2-subgroup of the symmetric group of degree 2^n.

Also the number of fixed-point free involutory automorphisms of the complete binary tree of height n.

Links

Table of n, a(n) for n=0..9.

Formula

a(n) = a(n-1)^2 + 2^(2^(n-1)-1), a(0) = 0.

a(n) ~ C^(2^n) for C = 1.467067423065535412629251121186749718727038915553188083467...

Example

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).

Mathematica

Nest[Append[#1, #1[[-1]]^2 + 2^(2^(#2 - 1) - 1)] & @@ {#, Length@ #} &, {0}, 9] (* Michael De Vlieger, Feb 25 2020 *)

Crossrefs

Cf. A332757.

Sequence in context: A349643 A098138 A009719 * A023150 A257116 A305375

Adjacent sequences: A332755 A332756 A332757 * A332759 A332760 A332761

Keyword

nonn

Author

Nick Krempel, Feb 22 2020

Status

approved