cp's OEIS Frontend

A179405 n-th derivative of x^(x^(x^x)) at x=1.

%I A179405 #28 Nov 15 2017 09:31:05
%S A179405 1,1,2,9,56,360,2934,26054,269128,3010680,37616880,504880992,
%T A179405 7387701672,115228447152,1929016301016,34194883090440,643667407174464,
%U A179405 12757366498618176,266426229010029696,5830527979298793024,133665090871032478080,3197905600674249843840
%N A179405 n-th derivative of x^(x^(x^x)) at x=1.
%C A179405 First term < 0: a(329). - _Alois P. Heinz_, Sep 22 2015
%H A179405 Alois P. Heinz, <a href="/A179405/b179405.txt">Table of n, a(n) for n = 0..400</a>
%F A179405 E.g.f.: (x+1)^((x+1)^((x+1)^(x+1))). - _Alois P. Heinz_, Aug 23 2012
%p A179405 a:= n-> n!*coeff(series(subs(x=x+1, x^(x^(x^x)) ), x, n+1), x, n):
%p A179405 seq(a(n), n=0..30);  # _Alois P. Heinz_, Aug 20 2012
%t A179405 f[n_] := D[ x^(x^(x^x)), {x, n}] /. x -> 1; Array[f, 18, 0]
%t A179405 Range[0, 21]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x)^(1 + x), {x, 0, 21}], x] (* _Robert G. Wilson v_, Feb 03 2013 *)
%Y A179405 Cf. A005727, A179230, A295104.
%Y A179405 Column k=8 of A215703.
%Y A179405 Column k=4 of A277537.
%K A179405 sign
%O A179405 0,3
%A A179405 _Robert G. Wilson v_, Jul 13 2010
%E A179405 a(18)-a(21) from _Alois P. Heinz_, Aug 20 2012