A277529 - OEIS

%I #11 May 23 2023 05:40:04

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

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

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

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

%H Alois P. Heinz, <a href="/A277529/b277529.txt">Table of n, a(n) for n = 5..1004</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 -50109.2762750366968958680172353229451272183942...

%t f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[8][f][1/2], 10, 120][[1]] (* _Amiram Eldar_, May 23 2023 *)

%Y Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277527, A277528, A277530, A277531.

%K nonn,cons

%O 5,1

%A _Alois P. Heinz_, Oct 19 2016