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%I #25 Sep 10 2018 03:02:19
%S 5,6,5,0,1,8,4,4,5,9,6,0,2,4,1,5,0,5,2,8,9,9,4,0,9,6,0,6,2,2,4,5,1,9,
%T 2,0,2,8,3,9,2,6,8,0,0,7,8,5,1,1,8,3,8,2,8,5,5,1,9,0,7,7,6,5,3,9,8,9,
%U 6,0,7,0,6,4,1,1,3,2,5,1,5,5,4,4,0,8,2,3,0,4,7,7,2,1,7,8,3,8,8,6,8,1,4,7,3,6
%N Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/Pi.
%H Alois P. Heinz, <a href="/A293009/b293009.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F Equals Pi*exp(-2*LambertW(log(Pi)))/(1+LambertW(log(Pi))).
%e 0.56501844596024150528994096062245192028392680078511838285519...
%t RealDigits[Pi*Exp[-2*LambertW[Log[Pi]]]/(1+LambertW[Log[Pi]]), 10, 100][[1]] (* _G. C. Greubel_, Sep 09 2018 *)
%o (PARI) Pi*exp(-2*lambertw(log(Pi)))/(1+lambertw(log(Pi))) \\ _Michel Marcus_, Mar 16 2018
%Y Cf. A000796, A049541, A073243, A277522, A277651, A300916.
%K nonn,cons
%O 0,1
%A _Alois P. Heinz_, Mar 16 2018