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 A000722 Number of invertible Boolean functions of n variables: a(n) = (2^n)!. (Formerly M2144 N0853) 21
 1, 2, 24, 40320, 20922789888000, 263130836933693530167218012160000000, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 (list; graph; refs; listen; history; text; internal format)
 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 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 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. Sequence in context: A137888 A229333 A108349 * A098679 A123851 A258824 Adjacent sequences:  A000719 A000720 A000721 * A000723 A000724 A000725 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)