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%I #25 Nov 15 2017 09:49:06
%S 1,1,2,9,56,480,5094,60494,823528,12365424,206078880,3745686912,
%T 74083090872,1579529362944,36165466533000,884104045301640,
%U 22992315801392064,633547543117707648,18439576158792912192,565162707747635408448,18194047307015185486080
%N n-th derivative of x^(x^(x^(x^(x^x)))) at x=1.
%H Robert G. Wilson v and Alois P. Heinz, <a href="/A211205/b211205.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)^(x+1))))).
%p a:= n-> n!*coeff(series(subs(x=x+1, x^(x^(x^(x^(x^x))))), x, n+1), x, n):
%p seq(a(n), n=0..20);
%t NestList[ Factor[ D[#1, x]] &, x^x^x^x^x^x, 9] /. (x -> 1) (* or quicker *)
%t Range[0, 20]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x)^(1 + x)^(1 + x)^(1 + x), {x, 0, 20}], x]
%Y Cf. A005727, A008405, A176118, A179230, A179405, A179505, A215522, A215524, A215629, A215643, A215691, A215704, A215705, A215706, A215707, A215708, A215709, A215710, A215522, A295106.
%Y Column k=37 of A215703.
%Y Column k=6 of A277537.
%K nonn
%O 0,3
%A _Alois P. Heinz_ and _Robert G. Wilson v_, Feb 04 2013
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