cp's OEIS Frontend

A218505 Decimal expansion of Sum_{k>=1} (H(k)/k)^2, where H(k) = Sum_{j=1..k} 1/j.

%I A218505 #45 Nov 01 2024 02:00:20
%S A218505 4,5,9,9,8,7,3,7,4,3,2,7,2,3,3,7,3,1,3,9,4,3,0,1,5,7,1,0,2,9,9,9,6,3,
%T A218505 5,8,6,7,9,2,6,9,1,5,4,5,6,5,4,5,8,9,3,5,7,6,5,2,6,4,8,9,1,5,6,3,7,5,
%U A218505 1,2,6,1,8,7,9,4,6,1,7,5,9,7,8,6,6,8,6,5,9,5,2,7,5,2,2,2,4,6,4,8
%N A218505 Decimal expansion of Sum_{k>=1} (H(k)/k)^2, where H(k) = Sum_{j=1..k} 1/j.
%H A218505 D. H. Bailey and J. M. Borwein, <a href="http://escholarship.org/uc/item/6b6986dn#page-9">Euler's Multi-Zeta Sums</a>
%H A218505 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A218505 Equals 17*zeta(4)/4.
%F A218505 Equals 17*Pi^4/360.
%F A218505 Equals (17/4) * Sum_{k>=1} 1/k^4.
%F A218505 Equals (17/(22*Pi)) * Integral_{t=0..Pi} (Pi-t)^2*log(2*sin(t/2))^2 dt.
%e A218505 4.5998737432723373139430157102999635867926915456545893...
%t A218505 17*Pi^4/360 // N[#, 100] & // RealDigits // First
%o A218505 (PARI) 17*Pi^4/360 \\ _Charles R Greathouse IV_, Sep 02 2024
%K A218505 nonn,cons
%O A218505 1,1
%A A218505 _Jean-François Alcover_, Mar 28 2013
%E A218505 Offset corrected by _Rick L. Shepherd_, Jan 01 2014