A244061 -id:A244061 - cp's OEIS frontend

A000722 Number of invertible Boolean functions of n variables: a(n) = (2^n)!.

1, 2, 24, 40320, 20922789888000, 263130836933693530167218012160000000, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000

Offset: 0

N. J. A. Sloane

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

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).

Delbert L. Johnson, Table of n, a(n) for n = 0..8
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.
Index entries for sequences related to Boolean functions

Cf. A000652, A000653, A000654, A001038, A001537, A046856, A046857, A244061.

a[n_] := Factorial[2^n]; Table[a[n],{n,0,6}] (* James C. McMahon, Dec 06 2023 *)

atonfact(a,n) = {sr=0; for(x=1,n, y =(a^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) }

a(n) = (2^n)!.

Sum of reciprocals = 0.54169146825401604874... - Cino Hilliard, Feb 08 2003

A244060 Sum of digits of (2^n)!.

Original entry on oeis.org

1, 2, 6, 9, 63, 108, 324, 828, 1989, 4635, 10845, 24363, 54279, 118827, 258705, 565389, 1216134, 2611359, 5584518, 11875977, 25184205, 53209728, 112069377, 235502361, 493827687, 1033041267, 2156974227, 4495662081, 9355185828, 19437382512, 40329016200

Offset: 0

Robert G. Wilson v, Jun 18 2014

			If n=4, 2^4! = 16! = 20922789888000, with digit sum 63. - _N. J. A. Sloane_, Jun 18 2014

Cf. A000722, A007953.

Cf. A116988, A244061.

f[n_] := Total[ IntegerDigits[ (2^n)!]]; Array[f, 20, 0]

a(n) = sumdigits((2^n)!); \\ Michel Marcus, Oct 25 2021

from math import factorial
def A244060(n): return sum(int(d) for d in str(factorial(2**n))) # Chai Wah Wu, Oct 26 2021

a(n) = A007953(A000722(n)). - Michel Marcus, Jun 19 2014

a(26)-a(30) from Chai Wah Wu, Oct 25 2021

cp's OEIS Frontend

A000722 Number of invertible Boolean functions of n variables: a(n) = (2^n)!.

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