login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A068985 Decimal expansion of 1/e. 41
3, 6, 7, 8, 7, 9, 4, 4, 1, 1, 7, 1, 4, 4, 2, 3, 2, 1, 5, 9, 5, 5, 2, 3, 7, 7, 0, 1, 6, 1, 4, 6, 0, 8, 6, 7, 4, 4, 5, 8, 1, 1, 1, 3, 1, 0, 3, 1, 7, 6, 7, 8, 3, 4, 5, 0, 7, 8, 3, 6, 8, 0, 1, 6, 9, 7, 4, 6, 1, 4, 9, 5, 7, 4, 4, 8, 9, 9, 8, 0, 3, 3, 5, 7, 1, 4, 7, 2, 7, 4, 3, 4, 5, 9, 1, 9, 6, 4, 3, 7, 4, 6, 6, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From the "derangements" problem: this is the probability that if a large number of people are given their hats at random, nobody gets his own hat.

Also, decimal expansion of cosh(1)-sinh(1). - Mohammad K. Azarian, Aug 15 2006

Also, this is lim_{n->inf}P(n), where P(n) is the probability that a random rooted forest on [n] be a tree. See image from Wikipedia link. - Washington Bomfim, Nov 01 2010

lim x -> infinity (1 - 1/x)^x = 1/e. - Arkadiusz Wesolowski, Feb 17 2012

Also, location of the minimum of x^x. - Stanislav Sykora, May 18 2012

Also, -1/e is the global minimum of x*log(x) at x = 1/e and the global minimum of x*e^x at x = -1. - Rick L. Shepherd, Jan 11 2014

REFERENCES

Mohammad K. Azarian, An Expansion of e, Problem # B-765, Fibonacci Quarterly, Vol. 32, No. 2, May 1994, p. 181. Solution appeared in Vol. 33, No. 4, Aug. 1995, p. 377. [From Mohammad K. Azarian, Feb 08 2009]

A. Hald, A History of Probability and Statistics and Their Applications Before 1750, Wiley, NY, 1990 (Chapter 19).

Jolley, Summation of Series, Dover (1961) eq (103) on page 20.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 65.

LINKS

Table of n, a(n) for n=0..104.

Gerard P. Michon, Final Answers: Inclusion-Exclusion

Eric Weisstein's World of Mathematics, Factorial Sums

Eric Weisstein's World of Mathematics, Sultan's Dowry Problem

Eric Weisstein's World of Mathematics, e

Wikipedia, Graph of probabilities [From Washington Bomfim, Nov 01 2010]

FORMULA

Equals 2*(1/3! + 2/5! + 3/7! + ...). [Jolley]

1 - sum(i = 1..infinity, (-1)^(i - 1)/i! ). [Michon]

EXAMPLE

1/e = 0.3678794411714423215955237701614608674458111310317678... = A135005/5.

MATHEMATICA

RealDigits[N[1/E, 6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)

PROG

(PARI)

default(realprecision, 110);

exp(-1) \\ Rick L. Shepherd, Jan 11 2014

CROSSREFS

Cf. A000166, A001113, A068996, A092553.

Sequence in context: A003458 A133339 A112267 * A081391 A073850 A048748

Adjacent sequences:  A068982 A068983 A068984 * A068986 A068987 A068988

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Apr 08 2002

EXTENSIONS

More terms from Rick L. Shepherd, Jan 11 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified September 17 07:07 EDT 2014. Contains 246836 sequences.