A215522 - OEIS

%I #33 Feb 07 2021 11:29:54

%S 1,1,4,18,100,650,4908,41090,382520,3863808,42409440,497972112,

%T 6259762320,83343114504,1175904241848,17442325040520,272149555445760,

%U 4438451554802880,75714874759039104,1343817666163911168,24837691533530152320,475811860099666527360

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

%C Also n-th derivative of (x^(x^x))^x = x^(x^x*x) at x=1.

%C First term < 0: a(65).

%H Alois P. Heinz, <a href="/A215522/b215522.txt">Table of n, a(n) for n = 0..400</a>

%F E.g.f.: (x+1)^((x+1)^(x+2)).

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

%p seq(a(n), n=0..30);

%t m = 21; CoefficientList[(x+1)^((x+1)^(x+2)) + O[x]^(m+1), x]*Range[0, m]! (* _Jean-François Alcover_, Feb 07 2021 *)

%Y Column k=6 of A215703.

%Y Cf. A005727, A179230, A179405, A215524.

%K sign

%O 0,3

%A _Alois P. Heinz_, Aug 14 2012