|
| |
|
|
A068985
|
|
Decimal expansion of 1/e.
|
|
36
| |
|
|
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
(list; constant; graph; refs; listen; history; 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 their own hat.
Also, decimal expansion of cosh(1)-sinh(1). - Mohammad K. Azarian (azarian(AT)evansville.edu), 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. [From W. Bomfim (webonfim(AT)bol.com.br), Nov 01 2010]
|
|
|
REFERENCES
| 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.
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 (azarian(AT)evansville.edu), Feb 08 2009]
|
|
|
LINKS
| 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 W. Bomfim (webonfim(AT)bol.com.br), 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]] (* From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 18 2009 *)
|
|
|
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,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 08 2002
|
| |
|
|
