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A098875
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Decimal expansion of Sum_{n>0} n/exp(n).
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2
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9, 2, 0, 6, 7, 3, 5, 9, 4, 2, 0, 7, 7, 9, 2, 3, 1, 8, 9, 4, 5, 4, 1, 3, 5, 2, 2, 7, 1, 6, 4, 9, 9, 6, 0, 2, 8, 8, 1, 6, 5, 5, 6, 2, 6, 6, 5, 0, 5, 5, 1, 1, 5, 2, 3, 5, 3, 9, 6, 0, 4, 0, 9, 7, 2, 2, 0, 4, 7, 1, 9, 7, 4, 6, 5, 0, 2, 4, 4, 5, 6, 8, 6, 7, 3, 6, 9, 9, 7, 3, 2, 8, 3, 4, 3, 4, 7, 9, 4, 7, 2, 5, 3, 9, 7
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OFFSET
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0,1
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COMMENTS
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The expression generating this constant is a first degree Eulerian polynomial, in the "variable" e, with coefficient {1}, generated from sum_{n>=0} n^m/e^n, with m=1. See A008292. It approximates m!. - Richard R. Forberg, Feb 15 2015
See A255169 for the second degree polynomial and value.
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LINKS
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FORMULA
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Equals exp(1)/(exp(1)-1)^2.
Equals (1/2)/(cosh(1)-1).
Equals LambertW(x)*LambertW(-1,x), where x = (1/(1-e))*exp(1/(1-e)) = -A073333*exp(-A073333). (End)
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EXAMPLE
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0.9206735942077923189454135227164996028816556266505511523539604097220...
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MAPLE
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g:=x->sum(n/exp(n), n=1..x); evalf[110](g(1500)); evalf[110](g(4000));
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MATHEMATICA
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PROG
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(PARI) 1+sumalt(n=1, bernreal(2*n)*(1-2*n)/(2*n)!) \\ Gleb Koloskov, Jul 12 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 03 2004
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STATUS
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approved
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