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Decimal expansion of sum_(n>=1) (H(n,2)/n^2) where H(n,2) = A007406(n)/A007407(n) is the n-th harmonic number of order 2.
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%I #14 Jul 04 2014 15:46:43

%S 1,8,9,4,0,6,5,6,5,8,9,9,4,4,9,1,8,3,5,1,5,3,0,0,6,4,6,8,9,4,7,0,4,3,

%T 8,2,9,8,5,5,8,1,4,1,6,5,8,5,7,7,7,2,0,8,8,4,4,5,2,0,8,3,7,7,0,2,7,2,

%U 1,1,0,7,8,3,2,7,1,9,5,4,8,1,4,7,4,5,9,1,8,6,2,8,9,7,9,7,4,8,5,5

%N Decimal expansion of sum_(n>=1) (H(n,2)/n^2) where H(n,2) = A007406(n)/A007407(n) is the n-th harmonic number of order 2.

%H Vincenzo Librandi, <a href="/A244664/b244664.txt">Table of n, a(n) for n = 1..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 23.

%F 7*Pi^4/360 = (7/4)*A013662.

%e 1.894065658994491835153006468947043829855814165857772088445208377027211...

%t RealDigits[7/4*Zeta[4], 10, 100] // First

%o (PARI) 7*zeta(4)/4 \\ _Michel Marcus_, Jul 04 2014

%Y Cf. A007406, A007407, A013662.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Jul 04 2014