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A000722
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Number of invertible Boolean functions of n variables: a(n) = (2^n)!.
(Formerly M2144 N0853)
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25
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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FORMULA
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a(n) = (2^n)!.
Sum of reciprocals = 0.54169146825401604874... - Cino Hilliard, Feb 08 2003
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MATHEMATICA
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a[n_] := Factorial[2^n]; Table[a[n], {n, 0, 6}] (* James C. McMahon, Dec 06 2023 *)
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PROG
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(PARI) atonfact(a, n) = {sr=0; for(x=1, n, y =(a^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) }
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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