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 A210247 Signs of the polylogarithm li(-n,-1/3). 3
 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS a(n) is the sign of s(n) = li(-n,-1/3) = Sum_{k>=1} ((-1)^k)*k^n/3^k. Should s(n) be 0, the sign would be set to 0 as well. However, it is not known whether this ever happens. LINKS Robert Israel, Table of n, a(n) for n = 0..2000 (n=0..199 from Stanislav Sykora) S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), Stan's Library Vol. I, April 2006, updated March 2012. See Eq.(29). Eric W. Weisstein, MathWorld: Polylogarithm MathOverflow, A remarkable almost-identity FORMULA a(n) = sign(A210246(n)). Conjecture: a(n) = (-1)^k*a(28k+n). - Mikhail Kurkov, Aug 27 2018 That is not quite true: the first counterexample is n=578, where a(578)=a(578+28)=-1. - Robert Israel, Sep 05 2018 EXAMPLE a(5) = sign(A210246(5)) = sign(104) = +1. MAPLE S:= series(4/(3 + exp(4*x)), x, 201): seq(signum(coeff(S, x, j)), j=0..200); # Robert Israel, Sep 05 2018 CROSSREFS Cf. A210246, A212846. Sequence in context: A242179 A319117 A210245 * A269529 A244513 A292117 Adjacent sequences:  A210244 A210245 A210246 * A210248 A210249 A210250 KEYWORD sign AUTHOR Stanislav Sykora, Mar 19 2012 STATUS approved

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Last modified November 12 12:43 EST 2018. Contains 317109 sequences. (Running on oeis4.)