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A000724 Invertible Boolean functions of n variables.
(Formerly M3175 N1287)
0

%I M3175 N1287

%S 1,3,196,3406687200,2141364232858913975435172249600,

%T 43025354066936633335853878219659247776604712057098163541301459387254457761792000000

%N Invertible Boolean functions of n variables.

%C Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of (C_2)^n on domain and F_n=[S_2]^(S_n) on range. - _Sean A. Irvine_, Mar 16 2011

%C Technical report version of Harrison's paper contains incorrect value for a(4). - _Sean A. Irvine_, Mar 16 2011

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

%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 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 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%F a(n) = ((2^n)! + (2^n-1) * (2^(n-1))! * 2^(2^(n-1)) * b(n)) / (n! * 2^(2*n)) where b(n) = n! * Sum_{k=0..floor((n-1)/2)} (2^(n-2*k)-1) / ((n - 2*k)! * k!). - _Sean A. Irvine_, Aug 20 2017

%t Table[((2^n)! + (2^n - 1) (2^(n - 1))! 2^(2^(n - 1)) * (n! * Sum[ (2^(n - 2 k) - 1)/((n - 2 k)!*k!), {k, 0, Floor[(n - 1)/2]}]))/(n! 2^(2 n)), {n, 6}] (* _Michael De Vlieger_, Aug 20 2017 *)

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Mar 15 2011

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Last modified July 12 12:18 EDT 2020. Contains 335661 sequences. (Running on oeis4.)