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%I #13 Sep 08 2022 08:46:08
%S 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,
%T 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,
%U 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
%N Decimal expansion of sum_(n>=1) (H(n)^3/(n+1)^3) where H(n) is the n-th harmonic number.
%H Vincenzo Librandi, <a href="/A244674/b244674.txt">Table of n, a(n) for n = 0..1000</a>
%H Philippe Flajolet, Bruno Salvy, <a href="http://algo.inria.fr/flajolet/Publications/FlSa98.pdf">Euler Sums and Contour Integral Representations</a>, Experimental Mathematics 7:1 (1998) page 27.
%F Equals 2*zeta(3)^2 - 11/5040*Pi^6.
%e 0.79161153152434211716617692742020206556997223833501687696290045428823...
%t RealDigits[2*Zeta[3]^2 - 33/16*Zeta[6], 10, 102] // First
%o (PARI) default(realprecision, 100); 2*zeta(3)^2 - 11/5040*Pi^6 \\ _G. C. Greubel_, Aug 31 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); 2*Evaluate(L,3)^2 - 11/5040*Pi(R)^6; // _G. C. Greubel_, Aug 31 2018
%Y Cf. A001008, A002805, A002117.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Jul 04 2014
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