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A247670 Decimal expansion of Sum_{n >= 0} (-1)^n*H(n)/(2n+1)^3, where H(n) is the n-th harmonic number.

%I A247670 #10 Aug 31 2018 15:29:18
%S A247670 0,2,8,5,7,4,1,7,0,6,3,6,2,4,3,5,9,0,9,9,9,0,8,4,2,9,5,1,2,5,0,4,4,3,
%T A247670 1,0,8,8,6,0,3,0,1,8,6,9,1,4,8,6,0,1,6,0,9,1,3,3,1,9,3,5,0,9,8,8,4,9,
%U A247670 8,4,2,4,1,7,2,1,7,2,9,5,1,6,9,9,9,7,3,8,0,5,8,8,2,1,2,4,9,0,1,2,4,1
%N A247670 Decimal expansion of Sum_{n >= 0} (-1)^n*H(n)/(2n+1)^3, where H(n) is the n-th harmonic number.
%H A247670 G. C. Greubel, <a href="/A247670/b247670.txt">Table of n, a(n) for n = 0..10000</a>
%H A247670 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) p. 34.
%F A247670 Equals -(Pi^3/16)*log(2) - (7*Pi/16)*zeta(3) + (1/512)*(PolyGamma(3, 1/4) - PolyGamma(3, 3/4)), where PolyGamma(n,z) gives the n-th derivative of the digamma function Psi^(n)(z).
%e A247670 -0.02857417063624359099908429512504431088603018691486...
%t A247670 s = -(Pi^3/16)*Log[2] - (7*Pi/16)*Zeta[3] + (1/512)*(PolyGamma[3, 1/4] - PolyGamma[3, 3/4]); Join[{0}, RealDigits[s, 10, 101] // First]
%Y A247670 Cf. A244667, A244674, A244675, A244676, A247669.
%K A247670 nonn,cons
%O A247670 0,2
%A A247670 _Jean-François Alcover_, Sep 22 2014