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A019739
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Decimal expansion of E/2.
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3
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1, 3, 5, 9, 1, 4, 0, 9, 1, 4, 2, 2, 9, 5, 2, 2, 6, 1, 7, 6, 8, 0, 1, 4, 3, 7, 3, 5, 6, 7, 6, 3, 3, 1, 2, 4, 8, 8, 7, 8, 6, 2, 3, 5, 4, 6, 8, 4, 9, 9, 7, 9, 7, 8, 7, 4, 8, 3, 4, 8, 3, 8, 1, 3, 8, 6, 2, 0, 3, 8, 3, 1, 5, 1, 7, 6, 7, 7, 3, 7, 9, 7, 2, 8, 5, 6, 9, 1, 0, 8, 9, 2, 6, 2, 5, 8, 3, 2, 1
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| e/2 = lim n -> infinity n*(e-(1+1/n)^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 17 2002
An unusual infinite product for this number: e/2=prod ((1/n)!)^mu(n), for n from 1 to infinity, where mu is the Mobius function (see Millane ref.). [John M. Campbell (jmaxwellcampbell(AT)gmail.com), June 14 2011]
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REFERENCES
| Jolley, Summation of Series, Dover (1961) eq. (161) on page 30.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,20000
R. P. Millane., A product form of the Möbius transform, Whistler Center for Carbohydrate Research, Purdue University, West Lafayette, USA.
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FORMULA
| 10*this constant = 5*exp(1) = sum_{j=0..infinity} j^3/j! [Jolley] - R. J. Mathar, Oct 03 2011
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EXAMPLE
| 1.359140914229522617680143735676331248878623546849979787483483813862038... = A001113/2. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
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MATHEMATICA
| N[Product[((1/n)!)^MoebiusMu[n], {n, 1, 200000}]] ( * From John M. Campbell, June 14 2011 * )
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PROG
| (PARI) { default(realprecision, 20080); x=exp(1)/2; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b019739.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
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CROSSREFS
| Cf. A006083 = Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
Sequence in context: A058642 A141251 A186190 * A101298 A200510 A138055
Adjacent sequences: A019736 A019737 A019738 * A019740 A019741 A019742
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KEYWORD
| nonn,cons
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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