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%I #19 Jun 11 2015 04:46:58
%S 5,4,0,0,8,7,1,9,0,4,1,1,8,1,5,4,1,5,2,4,6,6,0,9,1,1,1,9,1,0,4,2,7,0,
%T 0,5,2,0,2,9,4,3,7,7,1,0,1,9,1,6,7,0,5,7,0,9,3,1,7,0,6,0,1,4,4,8,4,4,
%U 8,5,1,5,9,5,0,7,5,8,1,7,7,8,9,8,8,7,4,7,9,2,0,0,0,0,6,2,0,6,2,7,7,6,7,0,0
%N Decimal expansion of a constant related to A107379.
%C Limit n->infinity (Integral_{x=0..1} Product_{k=1..n} x^k*(1-x^k) dx)^(1/n) = Limit n->infinity (A258191(n)/A258192(n))^(1/n) = 1/A258234 = 0.18515528932235959464731321119795428527382236445907508398560553036... .
%H StackExchange - Mathematica, <a href="http://mathematica.stackexchange.com/questions/38919/no-response-to-an-infinite-limit">No response to an infinite limit</a>
%F Equals limit n->infinity A107379(n)^(1/n).
%F Equals limit n->infinity A173519(n)^(1/n).
%e 5.4008719041181541524660911191042700520294...
%t r^2/(r-1) /.FindRoot[-PolyLog[2, 1-r] == Log[r]^2, {r, E}, WorkingPrecision->117] (* _Vaclav Kotesovec_, Jun 11 2015 *)
%Y Cf. A107379, A173519, A258191, A258192, A258268, A258788.
%K nonn,cons
%O 1,1
%A _Vaclav Kotesovec_, May 24 2015
%E More terms from _Vaclav Kotesovec_, Jun 09 2015