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A255696
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Decimal expansion of the Plouffe sum S(1,2) = Sum_{n >= 0} 1/(n*(exp(2*Pi*n)-1)).
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8
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1, 8, 7, 2, 6, 8, 2, 4, 4, 9, 7, 6, 8, 5, 4, 6, 1, 1, 5, 6, 3, 8, 5, 7, 9, 4, 7, 9, 9, 6, 1, 3, 9, 8, 8, 6, 9, 1, 6, 2, 8, 9, 5, 6, 5, 2, 6, 1, 9, 5, 6, 3, 8, 4, 1, 3, 3, 1, 5, 7, 4, 5, 3, 7, 8, 8, 4, 3, 1, 9, 5, 1, 7, 0, 9, 8, 0, 2, 2, 6, 7, 5, 1, 7, 0, 7, 2, 7, 8, 4, 0, 2, 4, 5, 6, 7, 9, 7, 9, 9, 8, 7, 4, 4
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OFFSET
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-2,2
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LINKS
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Table of n, a(n) for n=-2..101.
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 5.
Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]
Simon Plouffe, Identities inspired by Ramanujan Notebooks (part 2), April 2006
Linas Vepštas, On Plouffe’s Ramanujan Identities, arXiv:math/0609775 [math.NT]
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FORMULA
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This is the case k=1, m=2 of S(k,m) = Sum_{n >= 0} 1/(n^k*(exp(m*Pi*n)-1)).
Pi = 72*S(1,1) - 96*S(1,2) + 24*S(1,4).
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EXAMPLE
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0.00187268244976854611563857947996139886916289565261956384...
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MATHEMATICA
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digits = 104; S[1, 2] = NSum[1/(n*(Exp[Pi*n] - 1)), {n, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> digits]; RealDigits[S[1, 2], 10, digits] // First
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CROSSREFS
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Cf. A255695 (S(1,1)), A255697 (S(1,4)), A255698 (S(3,1)), A255699 (S(3,2)), A255700 (S(3,4)), A255701 (S(5,1)), A255702 (S(5,2)), A255703 (S(5,4)),
Sequence in context: A021538 A179044 A084254 * A144750 A198928 A155068
Adjacent sequences: A255693 A255694 A255695 * A255697 A255698 A255699
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Jean-François Alcover, Mar 02 2015
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STATUS
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approved
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