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A238167 Decimal expansion of sum_(n>=1) H(n,3)/n^5 where H(n,3) = A007408(n)/A007409(n) is the n-th harmonic number of order 3.

%I A238167 #9 Dec 30 2017 17:26:26
%S A238167 1,0,4,6,9,2,4,4,0,1,7,2,4,6,7,6,0,8,2,3,4,5,7,2,3,0,1,4,2,2,2,7,9,2,
%T A238167 3,2,9,6,1,9,5,9,8,4,0,2,2,6,4,1,4,7,7,1,4,7,4,8,3,3,2,5,0,9,5,0,5,1,
%U A238167 8,3,8,4,4,2,2,8,2,0,1,1,1,9,0,0,1,7,8,1,8,5,1,8,6,0,3,0,7,7,9,7
%N A238167 Decimal expansion of sum_(n>=1) H(n,3)/n^5 where H(n,3) = A007408(n)/A007409(n) is the n-th harmonic number of order 3.
%H A238167 G. C. Greubel, <a href="/A238167/b238167.txt">Table of n, a(n) for n = 1..10000</a>
%H A238167 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 16.
%F A238167 Equals 5*zeta(2)*zeta(5) + 2*zeta(3)*zeta(4) - 10*zeta(7).
%e A238167 1.046924401724676082345723014222792329619598402264...
%t A238167 RealDigits[5*Zeta[2]*Zeta[5] +2*Zeta[3]*Zeta[4] -10*Zeta[7],10,100][[1]]
%o A238167 (PARI) 5*zeta(2)*zeta(5) + 2*zeta(3)*zeta(4) - 10*zeta(7) \\ _G. C. Greubel_, Dec 30 2017
%Y A238167 Cf. A007408, A007409, A152648, A152649, A152651, A238166, A238168, A238169.
%K A238167 nonn,cons
%O A238167 1,3
%A A238167 _Jean-François Alcover_, Feb 19 2014