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A000310 Coefficients of iterated exponentials.

%I A000310 M3612 N1464 #37 Feb 12 2022 03:38:06
%S A000310 1,4,26,234,2696,37919,630521,12111114,264051201,6445170229,
%T A000310 174183891471,5164718385337,166737090160871,5822980248613990,
%U A000310 218756388226681557,8797723991458469015,377159237609540937788,17170729962232112834302,827382365085791968518198,42070004707327023844695198
%N A000310 Coefficients of iterated exponentials.
%D A000310 J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%D A000310 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000310 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000310 T. D. Noe, <a href="/A000310/b000310.txt">Table of n, a(n) for n=1..100</a>
%H A000310 P. J. Cameron, <a href="http://www.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 A000310 Jekuthiel Ginsburg, <a href="/A000405/a000405.pdf">Iterated exponentials</a>, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]
%H A000310 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=300">Encyclopedia of Combinatorial Structures 300</a>
%F A000310 E.g.f.: -log(1+log(1+log(1+log(1-x)))).
%t A000310 max = 20; CoefficientList[-Log[1 + Log[1 + Log[1 + Log[1 - x]]]]/x + O[x]^max, x]*Range[max]! (* _Jean-François Alcover_, Feb 07 2016 *)
%o A000310 (PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, abs(stirling(n, j, 1))*T(j, k-1)));
%o A000310 a(n) = T(n, 4); \\ _Seiichi Manyama_, Feb 11 2022
%o A000310 (PARI) my(x='x+O('x^40)); Vec(serlaplace(-log(1+log(1+log(1+log(1-x)))))); \\ _Michel Marcus_, Feb 11 2022
%Y A000310 a(n) = |A039816(n, 1)| (first column of triangle). Cf. A003713, A000268, A000359, A000406, A001765.
%K A000310 nonn
%O A000310 1,2
%A A000310 _N. J. A. Sloane_