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A363540
Decimal expansion of Sum_{k>=1} (H(k)^3 - (log(k) + gamma)^3)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and gamma is Euler's constant (A001620).
2
5, 8, 2, 1, 7, 4, 0, 0, 8, 5, 0, 4, 8, 6, 4, 6, 5, 2, 8, 8, 9, 6, 8, 6, 8, 6, 1, 5, 5, 0, 2, 0, 4, 1, 3, 4, 3, 1, 5, 0, 3, 3, 3, 2, 4, 3, 1, 9, 5, 7, 7, 0, 1, 1, 4, 4, 2, 4, 0, 3, 9, 2, 7, 6, 4, 7, 6, 4, 1, 3, 9, 7, 2, 2, 5, 9, 8, 1, 8, 9, 7, 4, 9, 5, 1, 8, 9, 0, 4, 2, 8, 5, 7, 4, 3, 2, 3, 1, 9, 0, 9, 6, 5, 9, 7
OFFSET
1,1
FORMULA
Equals -gamma_3 - 3*gamma*gamma_2 - 3*gamma^2*gamma_1 - (3/4)*gamma^4 + (43/8)*zeta(4), where gamma_1, gamma_2 and gamma_3 are the 1st, 2nd and 3rd Stieltjes constants (A082633, A086279, A086280).
EXAMPLE
5.82174008504864652889686861550204134315033324319577...
MATHEMATICA
RealDigits[-StieltjesGamma[3] - 3*EulerGamma*StieltjesGamma[2] - 3*EulerGamma^2*StieltjesGamma[1] - 3*EulerGamma^4/4 + 43*Zeta[4]/8, 10, 120][[1]]
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 09 2023
STATUS
approved