login
Decimal expansion of sum_(n>=1) (H(n,3)/n^3) where H(n,3) = A007408(n)/A007409(n) is the n-th harmonic number of order 3.
2

%I #16 Jul 04 2014 15:47:13

%S 1,2,3,1,1,4,1,9,3,0,2,0,9,0,4,1,6,8,6,8,1,4,1,0,1,5,0,4,2,9,8,9,5,4,

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

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

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

%H Vincenzo Librandi, <a href="/A244665/b244665.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 zeta(3)^2/2 + Pi^6/1890.

%e 1.2311419302090416868141015042989541775427764478983711179869214129514580195...

%t RealDigits[1/2*Zeta[3]^2 + 1/2*Zeta[6], 10, 103] // First

%o (PARI) zeta(3)^2/2 + Pi^6/1890 \\ _Michel Marcus_, Jul 04 2014

%Y Cf. A002117, A007408, A007409, A244664.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Jul 04 2014