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%I #11 May 23 2023 05:40:00
%S 8,4,4,6,1,7,0,8,6,7,1,0,9,3,6,1,1,9,7,5,1,5,8,2,0,7,1,1,4,9,3,8,3,2,
%T 2,3,9,5,4,6,1,0,0,2,1,7,3,6,6,2,7,5,5,1,8,4,4,1,7,2,9,4,8,3,6,5,8,0,
%U 2,4,8,4,2,5,9,8,1,7,4,6,6,3,5,1,9,8,8,5,9,6,2,2,4,9,1,5,0,1,6,9,8,4,3,5,1
%N Decimal expansion of the ninth derivative of the infinite power tower function x^x^x... at x = 1/2.
%H Alois P. Heinz, <a href="/A277530/b277530.txt">Table of n, a(n) for n = 6..1005</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>.
%e 844617.08671093611975158207114938322395461002...
%t f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[9][f][1/2], 10, 120][[1]] (* _Amiram Eldar_, May 23 2023 *)
%Y Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277527, A277528, A277529, A277531.
%K nonn,cons
%O 6,1
%A _Alois P. Heinz_, Oct 19 2016
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