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%I #15 Sep 22 2015 10:04:19
%S 1,1,2,15,80,590,5034,47110,511216,6019416,77899320,1092871824,
%T 16459538952,265695302808,4560878625744,83020743848760,
%U 1595943389477760,32291354360340672,685838983512807360,15248888357184824256,354130117874225585280,8571971677758345319680
%N n-th derivative of x^((x^x)^x) at x=1.
%C Also n-th derivative of x^(x^(x^2)) at x=1.
%C First term < 0: a(272).
%H Alois P. Heinz, <a href="/A215705/b215705.txt">Table of n, a(n) for n = 0..300</a>
%F E.g.f.: (x+1)^((x+1)^((x+1)^2)).
%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..25);
%t With[{nn=30},CoefficientList[Series[(x+1)^((x+1)^((x+1)^2)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 30 2013 *)
%Y Column k=7 of A215703.
%Y Cf. A005727, A179230, A179405, A215524.
%K sign
%O 0,3
%A _Alois P. Heinz_, Aug 21 2012
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