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%I #38 Nov 15 2017 09:18:53
%S 1,1,2,9,32,180,954,6524,45016,360144,3023640,27617832,271481880,
%T 2775329232,31188079272,350827041000,4441125248640,54110311240512,
%U 765546040603584,9938498593229568,156934910753107200,2128783325724881280,37775147271084647424
%N n-th derivative of x^(x^x) at x=1.
%C First term < 0: a(33) = -868875490363254484795699722301440.
%H Alois P. Heinz, <a href="/A179230/b179230.txt">Table of n, a(n) for n = 0..400</a>
%F E.g.f.: (x+1)^((x+1)^(x+1)). - _Alois P. Heinz_, Aug 21 2012
%p a:= n-> n!*coeff(series(subs(x=x+1, x^(x^x) ), x, n+1), x, n):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Aug 20 2012
%t Table[ D[ x^(x^x), {x, n}] /. x -> 1, {n, 0, 20}] (* _Robert G. Wilson v_, Jul 12 2010 *)
%t NestList[ Factor[ D[ #1, x]] &, x^x^x, 20] /. x -> 1 (* _Robert G. Wilson v_, Aug 10 2010 *)
%t Range[0, 22]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x), {x, 0, 22}], x] (* _Robert G. Wilson v_, Feb 03 2013 *)
%Y Cf. A005727. Column k=4 of A215703. Column k=3 of A277537.
%Y Cf. A295103.
%K sign
%O 0,3
%A Henryk Trappmann (bo198214(AT)gmail.com), Jul 03 2010
%E a(21)-a(22) from _Alois P. Heinz_, Aug 20 2012
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