%I #28 Nov 15 2017 09:31:05
%S 1,1,2,9,56,360,2934,26054,269128,3010680,37616880,504880992,
%T 7387701672,115228447152,1929016301016,34194883090440,643667407174464,
%U 12757366498618176,266426229010029696,5830527979298793024,133665090871032478080,3197905600674249843840
%N n-th derivative of x^(x^(x^x)) at x=1.
%C First term < 0: a(329). - _Alois P. Heinz_, Sep 22 2015
%H Alois P. Heinz, <a href="/A179405/b179405.txt">Table of n, a(n) for n = 0..400</a>
%F E.g.f.: (x+1)^((x+1)^((x+1)^(x+1))). - _Alois P. Heinz_, Aug 23 2012
%p a:= n-> n!*coeff(series(subs(x=x+1, x^(x^(x^x)) ), x, n+1), x, n):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Aug 20 2012
%t f[n_] := D[ x^(x^(x^x)), {x, n}] /. x -> 1; Array[f, 18, 0]
%t Range[0, 21]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x)^(1 + x), {x, 0, 21}], x] (* _Robert G. Wilson v_, Feb 03 2013 *)
%Y Cf. A005727, A179230, A295104.
%Y Column k=8 of A215703.
%Y Column k=4 of A277537.
%K sign
%O 0,3
%A _Robert G. Wilson v_, Jul 13 2010
%E a(18)-a(21) from _Alois P. Heinz_, Aug 20 2012