OFFSET
0,2
COMMENTS
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.
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
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Delbert L. Johnson, Table of n, a(n) for n = 0..8
M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
FORMULA
a(n) = (2^n)!.
Sum of reciprocals = 0.54169146825401604874... - Cino Hilliard, Feb 08 2003
MATHEMATICA
a[n_] := Factorial[2^n]; Table[a[n], {n, 0, 6}] (* James C. McMahon, Dec 06 2023 *)
PROG
(PARI) atonfact(a, n) = {sr=0; for(x=1, n, y =(a^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved