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%I #8 Sep 20 2016 13:17:18
%S 4,4,3,0,0,1,4,5,7,4,3,8,8,3,8,0,5,6,6,7,4,4,1,9,2,6,9,9,9,2,7,1,9,0,
%T 4,6,6,9,7,5,0,2,2,6,0,5,5,5,1,9,6,4,6,2,7,9,2,0,1,2,0,9,6,6,8,6,0,6,
%U 0,3,1,3,1,0,6,4,0,4,9,1,9,9,9,9,0,0,0,4,8,4,1,0,0,6,6,8,9,8,6,8,8,2,0,7,9,5,9,0,8,1,3,6,1,6,9,4,1,7,0,7
%N Decimal expansion of the power tower of 1/(2*Pi): the real solution to (2*Pi)^x*x = 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlouffesConstants.html">Plouffe's Constants</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>
%F Equals LambertW(log(2*Pi))/log(2*Pi).
%F Equals exp(-LambertW(A061444)).
%e (1/(2*Pi))^(1/(2*Pi))^(1/(2*Pi))^... = 0.443001457438838056674419269992719...
%t RealDigits[ProductLog[Log[2 Pi]]/Log[2 Pi], 10, 120][[1]]
%Y Cf. A019692, A073243, A061444, A086201.
%K nonn,cons
%O 0,1
%A _Ilya Gutkovskiy_, Sep 08 2016