login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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