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Continued fraction expansion of Sum_{n=1..infinity} (-1)^(n+1)/n^n = Integral_{x=0..1} x^(x) dx.
1

%I #8 Aug 03 2024 11:53:26

%S 0,1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,1,1,2,4,1,120,1,3,1,4,1,2,

%T 6,1,1,5,1,1,5,2,1,11,2,409,1,1,7,3,2,1,11,142,1,3,1,44,1,1,27,1,3,1,

%U 1,100,1,39,14,2,16,1,1,11,1,2,29,2,1,1,1,3,4,1,1,1,12,1,1,118,7,9,1,1,6

%N Continued fraction expansion of Sum_{n=1..infinity} (-1)^(n+1)/n^n = Integral_{x=0..1} x^(x) dx.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sophomore%27s_dream">Sophomore's dream</a>.

%p sd1 := proc(n) local i, tren; tren := 0: for i from 1 to n do tren := (-1)^(i+1)*(1/i^(i)) + tren: od; RETURN(tren); end: numtheory[cfrac] (sd1(300),150,'quotients');

%Y Cf. A083648 (decimal expansion).

%K nonn,cofr

%O 0,3

%A _Jani Melik_, Apr 16 2008

%E Offset changed by _Andrew Howroyd_, Aug 03 2024