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A068996
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Decimal expansion of 1 - 1/e.
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3
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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
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OFFSET
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0,1
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COMMENTS
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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. See image from Wikipedia. [From Washington Bomfim, Nov 01 2010]
Also equals the mode of a Gompertz distribution when the shape parameter is less than 1. [Jean-François Alcover, Apr 17 2013]
Equals -sum((-1)^k/k!, k=1..infinity). [Bruno Berselli, May 13 2013]
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..98.
B. Conrey & T. Davis, Derangements
J. Sondow and Eric Weisstein, e, MathWorld
Wikipedia, Graph of probabilities [From Washington Bomfim, Nov 01 2010]
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FORMULA
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integral(x = 0 .. 1, exp(-x) dx ) - Alonso del Arte, Jul 06 2012
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EXAMPLE
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.6321205588285576784044762...
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MATHEMATICA
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RealDigits[1 - 1/E, 10, 100][[1]] (* Alonso del Arte, Jul 06 2012 *)
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CROSSREFS
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Cf. A000166, A068985.
Sequence in context: A122178 A126445 A033326 * A068924 A106224 A226579
Adjacent sequences: A068993 A068994 A068995 * A068997 A068998 A068999
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KEYWORD
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nonn,cons,changed
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AUTHOR
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N. J. A. Sloane, Apr 08 2002
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STATUS
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approved
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