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A256987 Decimal expansion of Sum_{k>=1} H(k)*H(k,2)/k^2 where H(k) is the k-th harmonic number and H(k,2) the k-th harmonic number of order 2.

%I A256987 #14 Feb 16 2025 08:33:25
%S A256987 3,0,1,4,2,3,2,1,0,5,4,4,0,6,6,6,0,4,4,5,2,8,4,5,0,9,2,7,9,4,2,1,5,9,
%T A256987 7,4,0,1,3,9,2,3,2,3,8,6,1,6,2,0,4,7,0,2,0,6,7,0,0,1,4,9,5,4,9,5,8,5,
%U A256987 1,8,6,2,3,9,3,2,8,8,5,6,9,2,2,6,2,4,2,7,4,7,9,0,7,8,8,8,2,9,4,3,7,5,1,7,1
%N A256987 Decimal expansion of Sum_{k>=1} H(k)*H(k,2)/k^2 where H(k) is the k-th harmonic number and H(k,2) the k-th harmonic number of order 2.
%H A256987 Alois Panholzer and Helmut Prodinger, <a href="http://www.emis.de/journals/SLC/wpapers/s55panprod.pdf">Computer-free evaluation of an infinite double sum via Euler sums</a>, Séminaire Lotharingien de Combinatoire 55 (2005), Article B55a
%H A256987 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number.</a>
%F A256987 zeta(5) + zeta(2)*zeta(3) = zeta(5) + (Pi^2/6)*zeta(3).
%e A256987 3.01423210544066604452845092794215974013923238616204702067...
%t A256987 RealDigits[Zeta[5] + (Pi^2/6)*Zeta[3], 10, 105] // First
%o A256987 (PARI) zeta(5) + zeta(2)*zeta(3) \\ _Michel Marcus_, Apr 14 2015
%Y A256987 Cf. A002117, A013661, A013663, A152648, A152651, A238181, A244667, A256988.
%K A256987 nonn,cons,easy
%O A256987 1,1
%A A256987 _Jean-François Alcover_, Apr 14 2015