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%I #11 Nov 13 2021 05:55:35
%S 0,3,3,4,7,8,8,0,4,5,7,8,5,6,5,0,6,6,3,8,5,9,5,6,8,5,4,7,8,8,7,3,7,7,
%T 9,9,7,1,3,7,5,9,7,3,0,4,0,5,7,3,4,9,7,4,8,2,8,6,6,5,7,6,4,2,8,8,6,8,
%U 3,6,2,2,5,2,7,9,5,8,8,3,8,1,0,7,9,5,3,4,7,4,7,5,8,6,5,8,6,4,8,6,2,2,8,2,6,6,5,1,1,1,1,2,1,8,5,5,1,7,9,8,3
%N Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^4.
%C First derivative of the Dirichlet eta function at 4.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%F Equals (Pi^4 * log(2) + 630 * zeta'(4)) / 720.
%e 0.0334788045785650663859568547887377997137597304057...
%t Flatten[{0, RealDigits[(Pi^4 Log[2] + 630 Zeta'[4])/720, 10, 120][[1]]}]
%o (PARI) sumalt(k=1, (-1)^k * log(k) / k^4) \\ _Michel Marcus_, Nov 12 2021
%Y Cf. A013662, A091812, A210593, A256358, A261506, A267315, A349220.
%K nonn,cons
%O 0,2
%A _Ilya Gutkovskiy_, Nov 12 2021