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n-th derivative of x^((x^(x^x))^x) at x=1.
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%I #23 Feb 07 2021 07:04:12

%S 1,1,2,15,104,890,8814,100660,1288048,18337680,286674960,4882660464,

%T 89880715704,1777384045944,37552294300416,843830334815640,

%U 20086549955304384,504750167170162944,13348550475903813120,370499740676381737728,10766442934111876381440

%N n-th derivative of x^((x^(x^x))^x) at x=1.

%C Also n-th derivative of x^((x^x)^(x^x)) = x^(x^(x^x*x)) at x=1.

%H Alois P. Heinz, <a href="/A215643/b215643.txt">Table of n, a(n) for n = 0..400</a>

%F E.g.f.: (x+1)^(((x+1)^((x+1)^(x+1)))^(x+1)).

%p a:= n-> n!*coeff(series(subs(x=x+1, x^((x^(x^x))^x) ), x, n+1), x, n):

%p seq(a(n), n=0..30);

%t m = 20;

%t CoefficientList[(x+1)^(((x+1)^((x+1)^(x+1)))^(x+1)) + O[x]^(m+1), x]* Range[0, m]! (* _Jean-François Alcover_, Feb 07 2021 *)

%Y Column k=15 of A215703.

%Y Cf. A005727, A179230, A179405, A215522, A215524.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 18 2012