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A068996 Decimal expansion of 1 - 1/e. 7
6, 3, 2, 1, 2, 0, 5, 5, 8, 8, 2, 8, 5, 5, 7, 6, 7, 8, 4, 0, 4, 4, 7, 6, 2, 2, 9, 8, 3, 8, 5, 3, 9, 1, 3, 2, 5, 5, 4, 1, 8, 8, 8, 6, 8, 9, 6, 8, 2, 3, 2, 1, 6, 5, 4, 9, 2, 1, 6, 3, 1, 9, 8, 3, 0, 2, 5, 3, 8, 5, 0, 4, 2, 5, 5, 1, 0, 0, 1, 9, 6, 6, 4, 2, 8, 5, 2, 7, 2, 5, 6, 5, 4, 0, 8, 0, 3, 5, 6 (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, at least one person gets their own hat.

1-1/e is the limit to which (1 - !n/n!) {= 1 - A000166(n)/A000142(n) = A002467(n)/A000142(n)} converges as n tends to infinity. - Lekraj Beedassy, Apr 14 2005

Also, this is lim_{n->inf} P(n), where P(n) is the probability that a random rooted forest on [n] is not connected. - Washington Bomfim, Nov 01 2010

Also equals the mode of a Gompertz distribution when the shape parameter is less than 1. - Jean-Fran├žois Alcover, Apr 17 2013

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.3.

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

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

LINKS

Table of n, a(n) for n=0..98.

B. Conrey & T. Davis, Derangements

J. Sondow and Eric Weisstein, e, MathWorld

Bala Subramanian, Why time constant is 63.2% not a 50 or 70%? (2018)

FORMULA

integral(x = 0 .. 1, exp(-x) dx ). - Alonso del Arte, Jul 06 2012

Equals -sum(k>=1, (-1)^k/k! ). - Bruno Berselli, May 13 2013

Also equals Sum_{k>=0} ((1/((2*k+2)*(2*k)!). - Fred Daniel Kline, Mar 03 2016

EXAMPLE

0.6321205588285576784044762...

MATHEMATICA

RealDigits[1 - 1/E, 10, 100][[1]] (* Alonso del Arte, Jul 06 2012 *)

PROG

(PARI) 1 - exp(-1) \\ Michel Marcus, Mar 04 2016

CROSSREFS

Cf. A000166, A068985, A185393.

Sequence in context: A126445 A277435 A033326 * A068924 A106224 A254571

Adjacent sequences:  A068993 A068994 A068995 * A068997 A068998 A068999

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane, Apr 08 2002

STATUS

approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)