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 A000724 Invertible Boolean functions of n variables. (Formerly M3175 N1287) 0
 1, 3, 196, 3406687200, 2141364232858913975435172249600, 43025354066936633335853878219659247776604712057098163541301459387254457761792000000 (list; graph; refs; listen; history; text; internal format)
 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 F_n=[S_2]^(S_n) on range. - Sean A. Irvine, Mar 16 2011 Technical report version of Harrison's paper contains incorrect value for a(4). - Sean A. Irvine, Mar 16 2011 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 M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only] FORMULA 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 MATHEMATICA 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 *) CROSSREFS Sequence in context: A203749 A093978 A101382 * A309749 A209120 A256407 Adjacent sequences:  A000721 A000722 A000723 * A000725 A000726 A000727 KEYWORD nonn AUTHOR EXTENSIONS More terms from Sean A. Irvine, Mar 15 2011 STATUS approved

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Last modified May 29 10:05 EDT 2020. Contains 334699 sequences. (Running on oeis4.)