A000723 Invertible Boolean functions of n variables. (Formerly M3180 N1289)

1, 3, 840, 54486432000, 68523655451482690147713024000000, 2753622660283944533494648206058191857701074569760095316814277221684346880000000000000

Offset

1,2

Comments

Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of (C_2)^n on domain and permutation of variables on range. - Sean A. Irvine, Mar 15 2011

Also the number of distinct adjacency matrices of the n-hypercube graph Q_n. - Eric W. Weisstein, Mar 31 2017

References

M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..8

M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]

Eric Weisstein's World of Mathematics, Adjacency Matrix

Eric Weisstein's World of Mathematics, Hypercube Graph

Index entries for sequences related to Boolean functions

Formula

a(n) = (2^n-1)!/n! - Sean A. Irvine, Mar 15 2011

Mathematica

f[n_] := (2^n - 1)!/n!; Array[f, 6] (* Robert G. Wilson v, Mar 14 2011 *)
Table[Gamma[2^n]/n!, {n, 6}] ) (* Eric W. Weisstein, Mar 31 2017 *)

Prog

(Magma) [Factorial(2^n - 1)/Factorial(n): n in [1..10]]; // Vincenzo Librandi, Mar 28 2012

Crossrefs

Sequence in context: A062658 A266654 A332183 * A020525 A252762 A341574

Adjacent sequences: A000720 A000721 A000722 * A000724 A000725 A000726

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 14 2011

Status

approved