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 A352473 #9 Mar 18 2022 13:14:29
%S A352473 8,2,8,6,4,7,1,2,7,6,7,1,8,7,8,5,0,8,0,3,8,9,1,6,9,4,6,8,5,5,8,4,7,8,
%T A352473 9,1,8,8,3,6,1,6,6,5,9,4,0,1,5,5,8,8,2,7,9,4,5,6,3,9,6,5,8,9,7,1,3,7,
%U A352473 5,5,7,9,4,1,9,4,2,2,3,9,1,3,1,0,7,1,4,0,6,2,0,8,4,6,1,8,2
%N A352473 Decimal expansion of Sum_{k>=2} (log(k!) / k!).
%C A352473 Sum_{k>=2} (log(k) / k) is divergent but here, this series is convergent. If v(k) = log(k!) / k!, we have 0 <= v(k) <= w(k) = k^2/k! with w(k) that is convergent, hence, this positive series is convergent.
%D A352473 J.-M. Monier, Analyse, Tome 3, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 3.2.13.b p. 250.
%F A352473 Equals Sum_{k>=2} (log(k!) / k!).
%e A352473 0.8286471276718785080389169468558478918...
%p A352473 sum(log(n!)/n!, n=2..infinity);
%o A352473 (PARI) sumpos(k=2, log(k!)/k!) \\ _Michel Marcus_, Mar 17 2022
%Y A352473 Cf. A099769, A115563, A168218, A257812.
%K A352473 nonn,cons
%O A352473 0,1
%A A352473 _Bernard Schott_, Mar 17 2022