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A345385 Decimal expansion of Sum_{k>=2} zeta''(k).

%I A345385 #15 Jul 19 2021 03:45:06
%S A345385 2,3,3,6,3,1,3,1,7,6,0,5,8,9,3,3,2,9,1,9,9,6,5,1,5,4,8,1,3,7,7,7,1,2,
%T A345385 2,4,4,7,5,5,7,6,9,7,9,4,3,3,0,2,7,0,7,9,6,7,7,6,7,8,2,7,0,8,7,8,2,9,
%U A345385 2,8,9,1,6,3,6,9,0,1,4,0,0,2,7,2,1,3,5,9,7,4,0,7,0,6,0,8,3,1,4,7,9,3,6,2,2
%N A345385 Decimal expansion of Sum_{k>=2} zeta''(k).
%H A345385 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 538.
%H A345385 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a> 2011, p. 355.
%F A345385 Equals Sum_{k>=1} log(k+1)^2 / (k*(k+1)).
%e A345385 2.3363131760589332919965154813777122447557697943302707967767827087829289...
%p A345385 evalf(Sum(Zeta(2, k), k = 2..infinity), 120);
%t A345385 RealDigits[Sum[Zeta''[k], {k, 2, 1000}], 10, 110][[1]]
%o A345385 (PARI) suminf(k=2, zeta''(k))
%Y A345385 Cf. A085361, A131688, A345384.
%K A345385 nonn,cons
%O A345385 1,1
%A A345385 _Vaclav Kotesovec_, Jun 17 2021