A277525 - OEIS

%I #11 May 23 2023 05:39:12

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

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

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

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

%H Alois P. Heinz, <a href="/A277525/b277525.txt">Table of n, a(n) for n = 1..1000</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 -1.7296376776755434144759943668608340411378592485876...

%t f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[4][f][1/2], 10, 120][[1]] (* _Amiram Eldar_, May 23 2023 *)

%Y Cf. A033917, A104748, A277522, A277523, A277524, A277526, A277527, A277528, A277529, A277530, A277531.

%K nonn,cons

%O 1,2

%A _Alois P. Heinz_, Oct 19 2016