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A179505 n-th derivative of x^(x^(x^(x^x))) at x=1. 5

%I

%S 1,1,2,9,56,480,4374,47894,574888,7829424,116392080,1901059512,

%T 33564909432,639562529424,13047133134840,283976169754440,

%U 6563364026374464,160538113862231808,4141949353327046592,112396373034208003008,3199752121483607518080

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

%H Alois P. Heinz, <a href="/A179505/b179505.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)))). - _Alois P. Heinz_, Aug 21 2012

%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..25); # _Alois P. Heinz_, Aug 21 2012

%t f[n_] := D[x^(x^(x^(x^x))), {x, n}] /. x -> 1; Array[f, 16, 0]

%t Range[0, 20]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x)^(1 + x)^(1 + x), {x, 0, 20}], x] (* _Robert G. Wilson v_, Feb 03 2013 *)

%Y Cf. A005727, A179230, A179405, A295105.

%Y Column k=17 of A215703.

%Y Column k=5 of A277537.

%K nonn

%O 0,3

%A _Robert G. Wilson v_, Jul 17 2010

%E a(16)-a(20) from _Alois P. Heinz_, Aug 21 2012

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)