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 A354295 #9 May 23 2022 08:51:27
%S A354295 0,9,6,6,1,4,9,3,4,7,3,2,2,2,6,8,8,7,0,1,3,5,7,1,8,2,8,6,7,7,6,6,1,5,
%T A354295 5,0,0,5,6,3,3,8,3,1,9,4,9,6,8,3,5,5,3,5,4,7,3,1,5,6,8,0,3,8,6,1,3,2,
%U A354295 3,8,8,5,6,5,9,8,9,6,1,7,9,1,7,1,9,3,4,3,6,0,4,8,4,8,9,8,1,7,2,7,8,1,9,8,5,8
%N A354295 Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / (k+1).
%D A354295 A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 746, section 5.5.1, formula 4.
%e A354295 0.096614934732226887013571828677661550056338319496835535473156803861323...
%p A354295 evalf(Sum((-1)^k*log(k)/(k + 1), k = 1..infinity), 105);
%t A354295 N[NSum[(-1)^k*Log[k]/(k+1), {k, 1, Infinity}, WorkingPrecision -> 120, Method -> "AlternatingSigns"], 105]
%o A354295 (PARI) sumalt(k=1, (-1)^k*log(k)/(k+1))
%Y A354295 Cf. A091812, A257812.
%K A354295 nonn,cons
%O A354295 0,2
%A A354295 _Vaclav Kotesovec_, May 23 2022