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A210247 Signs of the polylogarithm li(-n,-1/3). 2
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

Given n, consider the series s(n) = li(-n,-1/3)) = SUM((-1)^k)(k^n)/3^k) for k=1,2,... Then the value of a(n) is the sign of s(n).

Should s(n) be 0, the sign would be set to 0 as well.

However, it is not known whether this ever happens.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..199

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

FORMULA

a(n) = sign(A210246(n)).

EXAMPLE

a(5) = sign(A210246(5)) = sign(104) = +1.

CROSSREFS

Cf. A210246, A212846.

Sequence in context: A262725 A242179 A210245 * A269529 A244513 A246016

Adjacent sequences:  A210244 A210245 A210246 * A210248 A210249 A210250

KEYWORD

sign

AUTHOR

Stanislav Sykora, Mar 19 2012

STATUS

approved

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Last modified May 23 04:09 EDT 2017. Contains 286909 sequences.