OFFSET
1,2
COMMENTS
As it appears that the Sum {n>=1} (-1)^(n+1)/n^2 / Sum {n>=1} ((-1)^(n+1))/n^1 is the inverse of Levy's constant, or more traditionally the log of Levy's constant (A100199), this sequence which is equal to Sum {n>=1} (-1)^(n+1)/n^3 / Sum {n>=1} ((-1)^(n+1))/n^1 may be the inverse of the log of another constant with similar properties.
FORMULA
EXAMPLE
1.300651149791018703323...
MATHEMATICA
RealDigits[3*Zeta[3]/(4*Log[2]), 10, 120][[1]] (* Amiram Eldar, May 27 2023 *)
PROG
(PARI) 3*zeta(3)/log(16) \\ Charles R Greathouse IV, Aug 05 2016
(PARI) sumalt(n=1, (-1)^n/n^3)/sumalt(n=1, (-1)^n/n) \\ Charles R Greathouse IV, Aug 05 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Terry D. Grant, Aug 05 2016
STATUS
approved