A000722 Number of invertible Boolean functions of n variables: a(n) = (2^n)!. (Formerly M2144 N0853)

1, 2, 24, 40320, 20922789888000, 263130836933693530167218012160000000, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000

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.

Index entries for sequences related to Boolean functions

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

Cf. A000652, A000653, A000654, A001038, A001537, A046856, A046857, A244061.

Sequence in context: A338152 A108349 A361431 * A098679 A123851 A258824

Adjacent sequences: A000719 A000720 A000721 * A000723 A000724 A000725

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved