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A348372
Decimal expansion of Sum_{k>=2} H(k)*H(k+1)/(k^3-k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
0
8, 8, 6, 7, 0, 9, 5, 8, 0, 1, 2, 8, 3, 4, 9, 1, 0, 5, 4, 8, 2, 1, 5, 8, 0, 4, 6, 8, 2, 7, 0, 4, 3, 7, 1, 1, 9, 3, 0, 2, 7, 6, 2, 3, 2, 3, 5, 7, 8, 0, 1, 5, 0, 8, 7, 7, 3, 8, 3, 8, 8, 8, 7, 3, 1, 5, 6, 5, 9, 9, 2, 6, 6, 1, 2, 8, 8, 6, 6, 9, 1, 3, 5, 5, 1, 3, 6, 9, 0, 1, 2, 3, 5, 7, 2, 5, 0, 6, 5, 5, 2, 7, 7, 9, 9
OFFSET
0,1
LINKS
Ovidiu Furdui and Alina Sȋntămărian, Problem 12060, The American Mathematical Monthly, Vol. 125, No. 7 (2018), p. 661; Summation by Parts and an Euler Sum, Solution to Problem 12060 by Omran Kouba, ibid., Vol. 127, No. 3 (2020), pp. 274-282.
FORMULA
Equals 5/2 - Pi^2/24 - zeta(3).
EXAMPLE
0.88670958012834910548215804682704371193027623235780...
MATHEMATICA
RealDigits[5/2 - Pi^2/24 - Zeta[3], 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Oct 15 2021
STATUS
approved