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URL: https://oeis.org/A238168

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A238168
Decimal expansion of sum_(n>=1) H(n)^2/n^5 where H(n) is the n-th harmonic number.
13
1, 0, 9, 1, 8, 8, 2, 5, 8, 8, 6, 6, 4, 5, 3, 0, 0, 8, 5, 1, 6, 5, 7, 8, 2, 1, 3, 0, 6, 9, 9, 2, 7, 3, 8, 7, 3, 3, 7, 7, 5, 6, 7, 8, 8, 9, 5, 3, 2, 4, 0, 8, 6, 2, 6, 3, 8, 1, 2, 6, 6, 6, 6, 7, 4, 7, 6, 6, 6, 6, 7, 7, 6, 8, 4, 0, 1, 2, 8, 5, 8, 2, 0, 4, 3, 6, 9, 1, 8, 0, 6, 7, 4, 2, 6, 5, 7, 5, 7, 8
OFFSET
1,3
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 16.
FORMULA
Equals 6*zeta(7) - zeta(2)*zeta(5) - 5/2*zeta(3)*zeta(4).
EXAMPLE
1.091882588664530085165782130699273873...
MATHEMATICA
RealDigits[6*Zeta[7] -Zeta[2]*Zeta[5] -(5/2)*Zeta[3]*Zeta[4], 10, 100][[1]]
PROG
(PARI) 6*zeta(7) - zeta(2)*zeta(5) - (5/2)*zeta(3)*zeta(4) \\ G. C. Greubel, Dec 30 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved