A134880 -id:A134880 - cp's OEIS frontend

A057156 Number of functions from {0,1}^n to {0,1}^n.

1, 4, 256, 16777216, 18446744073709551616, 1461501637330902918203684832716283019655932542976, 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816

Offset: 0

Henry Bottomley, Aug 15 2000

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

			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.
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

François Robert, Discrete Iterations: A Metric Study, Springer-Verlag, 1986, p. 167.
Norbert Wiener, Nonlinear Problems in Random Theory, MIT Press Classic, 1958, Lecture 1.

Alois P. Heinz, Table of n, a(n) for n = 0..8

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

lst={};Do[AppendTo[lst,(2^n)^(2^n)],{n,0,8}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 02 2009 *)

a(n)=1<<(n<Charles R Greathouse IV, Jan 19 2012

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

Sum_{n>=1} 1/a(n) = A134880. - Amiram Eldar, Nov 15 2020

More terms from Vladimir Joseph Stephan Orlovsky, Mar 02 2009

A134883 Decimal expansion of Sum_{n>=1} 1/(n^n+1).

Original entry on oeis.org

7, 3, 9, 9, 4, 7, 9, 4, 3, 4, 9, 5, 4, 6, 5, 5, 1, 2, 2, 5, 6, 0, 2, 5, 5, 3, 0, 7, 3, 4, 9, 9, 4, 7, 8, 2, 0, 5, 6, 1, 1, 0, 6, 6, 5, 7, 4, 2, 2, 4, 3, 9, 6, 2, 8, 7, 4, 5, 4, 5, 6, 5, 1, 9, 9, 9, 8, 0, 4, 3, 0, 8, 5, 4, 0, 8, 4, 8, 8, 1, 0, 2, 8, 9, 7, 3, 9, 5, 3, 1, 1, 2, 0, 7, 1, 2, 1, 5, 6, 8, 2, 0, 5, 9

Offset: 0

Artur Jasinski, Nov 15 2007

Constant formed from sum of reversed Sierpinski numbers of first kind A014566.

			0.7399479434954655122560255307349947820561106657422439628745456519998...

Cf. A014566, A073009, A100085, A134877, A134878, A134879, A134880, A134881, A134882.

RealDigits[N[Sum[1/(n^n + 1), {n, 1, 150}], 100]][[1]] (* first zero removed *)

A134882 Decimal expansion of Sum_{x>=1} 1/(Pi^x)^(Pi^x).

Original entry on oeis.org

0, 2, 7, 4, 2, 5, 6, 9, 3, 2, 7, 6, 9, 9, 1, 3, 7, 8, 2, 8, 1, 1, 6, 1, 1, 9, 4, 8, 4, 3, 1, 2, 0, 8, 3, 2, 6, 8, 2, 2, 5, 5, 9, 5, 3, 8, 8, 0, 5, 7, 8, 9, 0, 7, 0, 9, 9, 8, 8, 1, 7, 4, 4, 3, 1, 0, 1, 6, 1, 3, 8, 6, 5, 0, 3, 8, 8, 4, 7, 4, 4, 5, 7, 6, 3, 0, 8, 4, 3, 8, 8, 3, 2, 9, 1, 7, 4, 4, 7, 1, 1

Offset: 0

Artur Jasinski, Nov 14 2007

			0.02742569327699137828116119484312083268225595388057...

Cf. A073009, A100085, A134877, A134878, A134879, A134880, A134881, A134883.

RealDigits[N[Sum[1/(Pi^n)^(Pi^n), {n, 1, 20}], 200]][[1]] (* first two zeros removed *)

cp's OEIS Frontend

A057156 Number of functions from {0,1}^n to {0,1}^n.

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A134883 Decimal expansion of Sum_{n>=1} 1/(n^n+1).

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Author

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Comments

Examples

Crossrefs

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Mathematica

A134882 Decimal expansion of Sum_{x>=1} 1/(Pi^x)^(Pi^x).

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Author

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Crossrefs

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Mathematica