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A358191 Decimal expansion of Sum_{n >= 2} (n-1)/(n^n).

%I A358191 #13 Feb 16 2025 08:34:04
%S A358191 3,3,7,1,8,7,7,1,5,8,3,8,9,2,0,9,0,6,6,4,8,6,0,6,5,5,2,6,6,6,2,8,2,4,
%T A358191 9,0,1,5,1,9,2,0,9,4,2,6,8,0,0,9,9,0,9,9,1,6,4,1,3,3,9,8,4,9,5,5,4,4,
%U A358191 1,4,3,1,7,5,2,8,8,5,3,4,9,3,0,5,5,0,9,3,9,9,1,8,3,5,3,2,3,4,4,4
%N A358191 Decimal expansion of Sum_{n >= 2} (n-1)/(n^n).
%H A358191 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SophomoresDream.html">Sophomore's Dream</a>.
%F A358191 Equals Integral_{x = 0..1} x*log(x)^2/x^x dx.
%F A358191 Equals -Integral_{x = 0..1} x*log(x)/x^x dx.
%F A358191 Equals Integral_{x = 0..1} Integral_{y = 0..1} (x*y)^(1 - x*y) dy dx.
%F A358191 Equals A098686 - A073009.
%e A358191 0.337187715838920906648606552666282490151920942680099...
%p A358191 evalf(add((n-1)/n^n, n = 2..65), 100);
%o A358191 (PARI) suminf(n=2, (n-1)/n^n) \\ _Michel Marcus_, Nov 03 2022
%Y A358191 Cf. A073009, A098686.
%K A358191 cons,nonn
%O A358191 0,1
%A A358191 _Peter Bala_, Nov 02 2022