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%I M3991 N1654 #38 Feb 11 2022 12:42:57
%S 1,5,40,440,6170,105315,2120610,49242470,1296133195,38152216495,
%T 1242274374380,44345089721923,1722416374173854,72330102999829054,
%U 3265871028909088036,157797437377747327987,8124524883679977475839,444098724261935142753430
%N Coefficients of iterated exponentials.
%D J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A000359/b000359.txt">Table of n, a(n) for n=1..100</a>
%H 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 Jekuthiel Ginsburg, <a href="/A000405/a000405.pdf">Iterated exponentials</a>, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=301">Encyclopedia of Combinatorial Structures 301</a>
%F E.g.f.: -log(1+log(1+log(1+log(1+log(1-x))))).
%t max = 20; CoefficientList[-Log[1 + Log[1 + Log[1 + Log[1 + Log[1 - x]]]]]/x + O[x]^max, x]*Range[max]! (* _Jean-François Alcover_, Feb 08 2016 *)
%o (PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, abs(stirling(n, j, 1))*T(j, k-1)));
%o a(n) = T(n, 5); \\ _Seiichi Manyama_, Feb 11 2022
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-log(1+log(1+log(1+log(1+log(1-x))))))) \\ _Seiichi Manyama_, Feb 11 2022
%Y a(n) = |A039817(n, 1)| (first column of triangle). Cf. A003713, A000268, A000310, A000406, A001765.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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