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A244674
Decimal expansion of sum_(n>=1) (H(n)^3/(n+1)^3) where H(n) is the n-th harmonic number.
5
7, 9, 1, 6, 1, 1, 5, 3, 1, 5, 2, 4, 3, 4, 2, 1, 1, 7, 1, 6, 6, 1, 7, 6, 9, 2, 7, 4, 2, 0, 2, 0, 2, 0, 6, 5, 5, 6, 9, 9, 7, 2, 2, 3, 8, 3, 3, 5, 0, 1, 6, 8, 7, 6, 9, 6, 2, 9, 0, 0, 4, 5, 4, 2, 8, 8, 2, 3, 2, 5, 8, 5, 0, 2, 7, 4, 2, 0, 0, 3, 9, 5, 4, 9, 1, 6, 4, 8, 6, 7, 5, 3, 8, 8, 0, 6, 1, 7, 2, 1, 0, 1
OFFSET
0,1
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 27.
FORMULA
Equals 2*zeta(3)^2 - 11/5040*Pi^6.
EXAMPLE
0.79161153152434211716617692742020206556997223833501687696290045428823...
MATHEMATICA
RealDigits[2*Zeta[3]^2 - 33/16*Zeta[6], 10, 102] // First
PROG
(PARI) default(realprecision, 100); 2*zeta(3)^2 - 11/5040*Pi^6 \\ G. C. Greubel, Aug 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); 2*Evaluate(L, 3)^2 - 11/5040*Pi(R)^6; // G. C. Greubel, Aug 31 2018
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved