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A241753 Decimal expansion of Sum_{n>=1} (H(n)/(n+1))^2, where H(n) is the n-th harmonic number.

%I A241753 #11 May 26 2025 15:25:39
%S A241753 2,9,7,6,3,8,8,8,9,2,7,0,5,6,3,0,0,2,6,6,6,9,0,1,0,1,6,5,4,8,8,2,1,1,
%T A241753 7,3,2,6,3,0,5,6,5,1,1,7,7,7,6,4,9,8,9,9,6,1,2,8,1,8,4,5,9,2,4,7,1,3,
%U A241753 3,1,6,9,4,5,1,4,1,6,4,3,2,8,0,3,1,5,0,1,4,9,8,8,3,9,6,7,4,7,7,2
%N A241753 Decimal expansion of Sum_{n>=1} (H(n)/(n+1))^2, where H(n) is the n-th harmonic number.
%H A241753 David H. Bailey and Jonathan M. Borwein, <a href="http://www.ams.org/notices/200505/fea-borwein.pdf">Experimental Mathematics: Examples, Methods and Implications</a>, Notices of the AMS Volume 52, Number 5, page 506.
%F A241753 Equals 1/(2*Pi)*Integral_{x=0..Pi} (Pi-t)^2*log(2*sin(t/2))^2 dt.
%F A241753 Equals 11/17*A218505.
%F A241753 Equals 11*Pi^4/360. - _Vaclav Kotesovec_, Apr 28 2014
%e A241753 2.97638889270563002666901016548821173263...
%t A241753 RealDigits[11*Pi^4/360, 10, 100] // First
%o A241753 (PARI) 11*Pi^4/360 \\ _Stefano Spezia_, May 26 2025
%Y A241753 Cf. A218505.
%K A241753 nonn,cons
%O A241753 1,1
%A A241753 _Jean-François Alcover_, Apr 28 2014