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Decimal expansion of the tenth derivative of the infinite power tower function x^x^x... at x = 1/2, negated.
10

%I #11 May 23 2023 05:39:57

%S 1,4,1,0,9,5,0,8,6,0,4,5,7,8,2,5,2,1,6,6,7,4,8,0,7,9,5,6,6,6,2,1,3,8,

%T 6,1,1,5,9,2,7,6,0,7,4,9,5,2,5,0,6,8,9,5,9,1,6,1,0,1,8,4,7,0,8,2,4,0,

%U 0,4,4,5,8,4,4,8,8,7,2,4,0,0,8,9,3,2,4,1,1,6,2,1,3,3,3,3,4,9,8,0,6,7,0,5,3

%N Decimal expansion of the tenth derivative of the infinite power tower function x^x^x... at x = 1/2, negated.

%H Alois P. Heinz, <a href="/A277531/b277531.txt">Table of n, a(n) for n = 8..1007</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 -14109508.6045782521667480795666213861159276...

%t f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[10][f][1/2], 10, 120][[1]] (* _Amiram Eldar_, May 23 2023 *)

%Y Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277527, A277528, A277529, A277530.

%K nonn,cons

%O 8,2

%A _Alois P. Heinz_, Oct 19 2016