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%I #19 Jun 18 2023 03:00:30
%S 9,7,1,4,9,9,0,3,4,2,8,3,3,0,8,7,5,7,2,2,2,6,2,5,0,6,2,3,1,4,7,5,4,5,
%T 8,0,0,2,2,5,5,1,0,1,4,8,9,7,0,2,3,9,8,4,2,9,0,8,9,0,4,2,5,5,9,4,0,8,
%U 4,1,1,7,0,0,9,9,5,5,4,2,4,3,7,3,0
%N Decimal expansion of Sum_{k>=1} (k^(1/k^2) - 1).
%F Equals Sum_{k>=1} (-1)^k / k! * k-th derivative of zeta(2*k). - _Vaclav Kotesovec_, Jun 18 2023
%e 0.971499034283308757222625062314754580022...
%t digits = 120; d = 1; j = 2; s = Pi^2 * (2*Log[Glaisher] - Log[2*Pi]/6 - EulerGamma/6); While[Abs[d] > 10^(-digits - 5), d = (-1)^j/j!*Derivative[j][Zeta][2*j]; s += d; j++]; RealDigits[s, 10, 120][[1]] (* _Vaclav Kotesovec_, Jun 18 2023 *)
%o (PARI) sumpos(k=1, k^(1/k^2) - 1) \\ _Michel Marcus_, Nov 05 2019
%Y Cf. A073002, A098572.
%K nonn,cons
%O 0,1
%A _Daniel Hoyt_, Nov 05 2019
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