OFFSET
0
COMMENTS
Given an integer n, consider the infinite series s(n) = li(-n,-1/2) = Sum_{k>=0} (-1)^k*k^n/2^k. 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
Stanislav 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 Weisstein's World of Mathematics, Polylogarithm
FORMULA
a(n) is the same as the sign of cos((n+1)*arctan(Pi/log(2))). - Mikhail Kurkov, Apr 13 2021 [verification needed]
EXAMPLE
a(5) = sign(A212846(5)) = sign(-7) = -1.
MATHEMATICA
Join[{1}, Sign[PolyLog[-Range[80], -1/2]]] (* Harvey P. Dale, Jul 21 2024 *)
CROSSREFS
KEYWORD
sign,changed
AUTHOR
Stanislav Sykora, Mar 19 2012
STATUS
approved