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A215691 n-th derivative of (x^x)^(x^(x^x)) at x=1. 3


%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-Fran├žois 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

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Last modified April 20 13:26 EDT 2021. Contains 343135 sequences. (Running on oeis4.)