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A260272 Decimal expansion of Sum_{n>=1} H(n)^2/(n+1)^4, where H(n) is the n-th harmonic number.

%I A260272 #11 Apr 27 2025 01:06:44
%S A260272 1,2,3,4,6,3,0,8,8,7,9,2,3,9,1,5,2,3,1,4,6,1,9,6,7,2,9,6,2,0,6,8,1,3,
%T A260272 1,9,9,9,8,2,3,3,2,2,4,7,0,3,4,2,7,2,3,3,7,0,8,9,4,5,8,6,1,7,7,4,7,6,
%U A260272 1,5,9,2,5,0,9,1,6,4,3,2,3,9,3,6,4,1,6,7,8,4,1,3,6,7,2,4,2,4,0,5,7,4,2,4,8
%N A260272 Decimal expansion of Sum_{n>=1} H(n)^2/(n+1)^4, where H(n) is the n-th harmonic number.
%H A260272 Jason Bard, <a href="/A260272/b260272.txt">Table of n, a(n) for n = 0..10000</a>
%H A260272 David H. Bailey and J. M. Borwein, <a href="http://www.davidhbailey.com/dhbpapers/pslq-comp-alg.pdf">PSLQ: An Algorithm to Discover Integer Relations</a>
%F A260272 (37/22680)*Pi^6 - zeta(3)^2.
%e A260272 0.1234630887923915231461967296206813199982332247034272337089458617747615925...
%t A260272 RealDigits[(37/22680)*Pi^6 - Zeta[3]^2, 10, 105] // First
%Y A260272 Cf. A244676.
%K A260272 nonn,cons,easy
%O A260272 0,2
%A A260272 _Jean-François Alcover_, Jul 22 2015