%I #13 Sep 22 2015 15:52:29

%S 1,1,2,12,156,3160,87990,3218628,150271520,8710554816,610951827960,

%T 50770346742720,4919197411068072,548907184341479808,

%U 69823173142960626480,10034787531626188107840,1616352219917942008147200,289720383156740969786941440

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

%C x^(x^(n-1)) = (((x^x)^x)^ ... )^x with n x's.

%H Alois P. Heinz, <a href="/A216351/b216351.txt">Table of n, a(n) for n = 0..275</a>

%F a(n) = n! * [x^n] (x+1)^((x+1)^(n-1)).

%F a(n) = A216349(n,1) = A216350(n,A000081(n)) for n>0.

%p a:= n-> n! *coeff(series( (x+1)^((x+1)^(n-1)) , x, n+1), x, n):

%p seq(a(n), n=0..20);

%Y Cf. A000081, A216349, A216350, A215703.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 04 2012