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A377312
Decimal expansion of Sum_{k,m>=1} (-1)^(k+m) * H(k) * H(m) / (k+m+1)^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
0
3, 2, 3, 0, 7, 2, 9, 9, 7, 2, 9, 6, 1, 0, 1, 9, 5, 5, 8, 5, 5, 0, 1, 5, 8, 9, 7, 5, 6, 3, 7, 3, 9, 3, 5, 6, 9, 0, 0, 6, 5, 5, 7, 4, 4, 7, 2, 6, 6, 8, 4, 8, 7, 7, 2, 1, 6, 6, 8, 6, 4, 8, 7, 4, 6, 2, 6, 9, 7, 7, 9, 2, 1, 7, 4, 6, 8, 4, 3, 1, 6, 5, 0, 2, 8, 4, 0, 0, 7, 1, 9, 6, 7, 4, 6, 7, 1, 4, 8, 0, 6, 1, 8, 6, 3
OFFSET
-1,1
LINKS
Paul Bracken, Problem 4927, Crux Mathematicorum, Vol. 50, No. 3 (March, 2024), p. 149; Theo Koupelis, Solution to Problem 4927, ibid., Vol. 50, No. 8 (Oct. 2024), pp. 423-426.
FORMULA
Equals log(2)^3/3 + log(2)^2 + 2*log(2) - zeta(2) - zeta(3)/4.
EXAMPLE
0.032307299729610195585501589756373935690065574472668...
MATHEMATICA
RealDigits[Log[2]^3/3 + Log[2]^2 + 2*Log[2] - Zeta[2] - Zeta[3]/4, 10, 120][[1]]
PROG
(PARI) log(2)^3/3 + log(2)^2 + 2*log(2) - zeta(2) - zeta(3)/4
KEYWORD
nonn,cons,easy
AUTHOR
Amiram Eldar, Oct 24 2024
STATUS
approved