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Number of functions from {0,1}^n to {0,1}^n.
9

%I #25 Sep 06 2023 22:38:11

%S 1,4,256,16777216,18446744073709551616,

%T 1461501637330902918203684832716283019655932542976,

%U 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816

%N Number of functions from {0,1}^n to {0,1}^n.

%C a(n) is the number of subdivisions of the Brownian motion on the unit interval at the n-th stage of subdivision. - _Stephen Crowley_, Apr 12 2007

%D François Robert, Discrete Iterations: A Metric Study, Springer-Verlag, 1986, p. 167.

%D Norbert Wiener, Nonlinear Problems in Random Theory, MIT Press Classic, 1958, Lecture 1.

%H Alois P. Heinz, <a href="/A057156/b057156.txt">Table of n, a(n) for n = 0..8</a>

%F a(n) = (2^n)^(2^n) = A000312(A000079(n)) = A000079(A036289(n)) = A001146(n)^n = A000722(n) + A057157(n).

%F Sum_{n>=1} 1/a(n) = A134880. - _Amiram Eldar_, Nov 15 2020

%e a(1)=4 since the possibilities are f(0)=0, f(1)=0; f(0)=0, f(1)=1; f(0)=1, f(1)=0; f(0)=1, f(1)=1.

%e For n=3: we need to count maps from a set with 8 points to a set with 8 points. There are 8^8 such functions, that is, a(3) = 8^8 = 2^24 = 16777216. - _N. J. A. Sloane_, Mar 05 2023

%t lst={};Do[AppendTo[lst,(2^n)^(2^n)],{n,0,8}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 02 2009 *)

%o (PARI) a(n)=1<<(n<<n) \\ _Charles R Greathouse IV_, Jan 19 2012

%Y Cf. A000079, A000312, A000722, A001146, A036289, A043322, A057157, A092258, A134880.

%K easy,nice,nonn

%O 0,2

%A _Henry Bottomley_, Aug 15 2000

%E More terms from _Vladimir Joseph Stephan Orlovsky_, Mar 02 2009