This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A354592 #10 Jun 01 2022 07:59:23
%S A354592 1,0,3,0,5,4,2,3,5,3,7,8,4,9,4,1,2,0,8,9,9,6,2,8,0,9,2,9,8,2,8,8,7,4,
%T A354592 6,0,7,8,2,8,1,1,0,5,5,4,1,4,5,3,5,6,7,1,3,6,3,1,9,2,1,6,4,4,6,1,6,6,
%U A354592 7,5,1,0,9,5,0,4,0,4,8,3,2,9,0,2,5,7,5,5,5,4,7,4,0,0,3,0,3,0,7,4,9,0,2,4,3
%N A354592 Decimal expansion of Sum_{k>=1} (1/k - (1 - log(k)/k)^k).
%e A354592 1.030542353784941208996280929828874607828110554145356713631921644616675...
%p A354592 Digits := 120: ser := sort(convert(series((1/n - (1 - log(n)/n)^n), n = infinity, 300), polynom), n): s := evalf(sum(op(1, ser), n = 1..infinity), 120): for k from 2 to nops(ser) do serx := expand(op(k, ser)): for j to nops(serx) do s := s + evalf(sum(op(j, serx), n = 1..infinity), 120) end do: print(k, s) end do:
%t A354592 NSum[1/k - (1 - Log[k]/k)^k, {k, 1, Infinity}, WorkingPrecision -> 30, NSumTerms -> 100] (* only 20 digits are correct *)
%Y A354592 Cf. A354450, A354593.
%K A354592 nonn,cons
%O A354592 1,3
%A A354592 _Vaclav Kotesovec_, Jun 01 2022