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E.g.f.: -log(1+log(1+log(1-x))).
(Formerly M3003 N1218)
12

%I M3003 N1218 #45 Feb 11 2022 08:14:19

%S 1,3,15,105,947,10472,137337,2085605,36017472,697407850,14969626900,

%T 352877606716,9064191508018,252024567201300,7542036496650006,

%U 241721880399970938,8261159383595659128,299916384730043070880,11526945327529620432872,467583770376898192016104

%N E.g.f.: -log(1+log(1+log(1-x))).

%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 Seiichi Manyama, <a href="/A000268/b000268.txt">Table of n, a(n) for n = 1..400</a> (terms 1..100 from T. D. Noe)

%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=299">Encyclopedia of Combinatorial Structures 299</a>

%H Kruchinin Vladimir Victorovich, <a href="http://arxiv.org/abs/1009.2565">Composition of ordinary generating functions</a>, arXiv:1009.2565 [math.CO], 2010.

%F a(n) = sum((m-1)!*(-1)^(n+m)*sum(stirling1(n, k)*stirling1(k, m), k,m,n), m,1,n), n>0. - _Vladimir Kruchinin_, Sep 14 2010

%t max = 20; CoefficientList[-Log[1 + Log[1 + Log[1 - x]]]/x + O[x]^max, x] * Range[max]! (* _Jean-François Alcover_, Feb 06 2016 *)

%o (PARI) a(n) = sum(m=1, n, (m-1)!*(-1)^(n+m)*sum(k=m, n, stirling(n,k,1)*stirling(k,m,1))); \\ _Michel Marcus_, Feb 06 2016

%Y a(n)=|A039815(n, 1)| (first column of triangle).

%Y Cf. A003713, A000310, A000359, A000406, A001765.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Revised description from _Christian G. Bower_, Aug 15 1998