%I #23 Feb 07 2021 07:04:20
%S 1,1,4,18,124,950,8688,89600,1038392,13309272,186471480,2837173152,
%T 46466835072,815532508440,15246845864040,302533865599800,
%U 6344720827608384,140208886623418752,3254819745378435264,79172189409906466560,2013138139856523598080
%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="/A215691/b215691.txt">Table of n, a(n) for n = 0..400</a>
%F E.g.f.: (x+1)^((x+1)^((x+1)^(x+1)+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)+1)) + O[x]^(m+1), x]*Range[0, m]! (* _Jean-François Alcover_, Feb 07 2021 *)
%Y Column k=13 of A215703.
%Y Cf. A005727, A179230, A179405, A215522, A215524, A215643.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 20 2012