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n-th derivative of x^(x^((x^x)^x)) at x=1.
3

%I #21 Feb 07 2021 07:04:00

%S 1,1,2,9,80,660,6714,77084,1005640,14572944,233086920,4066783512,

%T 76906345944,1566049091568,34153725715368,793996577407560,

%U 19595885746343808,511550462381982528,14080034085212120256,407434430977558009344,12363449947108075756800

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

%H Alois P. Heinz, <a href="/A215629/b215629.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=16 of A215703.

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

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 18 2012