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A000406 Coefficients of iterated exponentials.

%I A000406 M4264 N1782 #32 Feb 11 2022 12:40:56
%S A000406 1,6,57,741,12244,245755,5809875,158198200,4877852505,168055077875,
%T A000406 6400217406500,267058149580823,12118701719205803,594291742526530761,
%U A000406 31323687504696772151,1766116437541895988303,106080070002238888908150
%N A000406 Coefficients of iterated exponentials.
%D A000406 J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%D A000406 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000406 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000406 T. D. Noe, <a href="/A000406/b000406.txt">Table of n, a(n) for n=1..100</a>
%H A000406 P. J. Cameron, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H A000406 Jekuthiel Ginsburg, <a href="/A000405/a000405.pdf">Iterated exponentials</a>, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]
%H A000406 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=302">Encyclopedia of Combinatorial Structures 302</a>
%F A000406 E.g.f.: -log(1+log(1+log(1+log(1+log(1+log(1-x)))))).
%t A000406 With[{nn=20},CoefficientList[Series[-Log[1+Log[1+Log[1+Log[1+ Log[1+ Log[1- x]]]]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 03 2015 *)
%o A000406 (PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, abs(stirling(n, j, 1))*T(j, k-1)));
%o A000406 a(n) = T(n, 6); \\ _Seiichi Manyama_, Feb 11 2022
%o A000406 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-log(1+log(1+log(1+log(1+log(1+log(1-x)))))))) \\ _Seiichi Manyama_, Feb 11 2022
%Y A000406 Cf. A003713, A000268, A000310, A000359, A001765.
%K A000406 nonn
%O A000406 1,2
%A A000406 _N. J. A. Sloane_