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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.
7
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