|
%I M2144 N0853 #52 Mar 25 2024 00:15:35
%S 1,2,24,40320,20922789888000,263130836933693530167218012160000000,
%T 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000
%N Number of invertible Boolean functions of n variables: a(n) = (2^n)!.
%C These are invertible maps from {0,1}^n to {0,1}^n, or in other words permutations of the 2^n binary vectors of length n.
%C 2^n-th order derivative of n-th Mandelbrot iterate. Example: a(2) = 24, after one iterate in the Mandelbrot(z(n+1) = z(n)^2 + c) we have the function z(2) = z^4 + 2*c*z^2 + c^2 + c, for which the 4th-order derivative is 24. - Bert van den Bosch (zeusooooo(AT)hotmail.com), Sep 07 2003
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Delbert L. Johnson, <a href="/A000722/b000722.txt">Table of n, a(n) for n = 0..8</a>
%H M. A. Harrison, <a href="/A000653/a000653.pdf">The number of classes of invertible Boolean functions</a>, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]
%H C. S. Lorens, <a href="http://dx.doi.org/10.1109/PGEC.1964.263724">Invertible Boolean functions</a>, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
%H C. S. Lorens, <a href="/A000722/a000722.pdf">Invertible Boolean functions</a>, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]
%H I. Strazdins, <a href="http://dx.doi.org/10.1023/A:1005769927571">Universal affine classification of Boolean functions</a>, Acta Applic. Math. 46 (1997), 147-167.
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%F a(n) = (2^n)!.
%F Sum of reciprocals = 0.54169146825401604874... - _Cino Hilliard_, Feb 08 2003
%t a[n_] := Factorial[2^n]; Table[a[n],{n,0,6}] (* _James C. McMahon_, Dec 06 2023 *)
%o (PARI) atonfact(a,n) = {sr=0; for(x=1,n, y =(a^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) }
%Y Cf. A000652, A000653, A000654, A001038, A001537, A046856, A046857, A244061.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
