cp's OEIS Frontend

A001765 Coefficients of iterated exponentials.

%I A001765 M4447 N1882 #33 Jan 07 2023 14:48:25
%S A001765 1,7,77,1155,21973,506989,13761937,429853851,15192078027,599551077881,
%T A001765 26140497946017,1248134313062231,64783855286002573,
%U A001765 3632510833677434324,218845138322691595694,14099918095287618382033,967508237903439910445565,70447525748137979196484589
%N A001765 Coefficients of iterated exponentials.
%D A001765 J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%D A001765 T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
%D A001765 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001765 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001765 T. D. Noe, <a href="/A001765/b001765.txt">Table of n, a(n) for n=1..100</a>
%H A001765 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 A001765 T. Hogg and B. A. Huberman, <a href="/A000258/a000258.pdf">Attractors on finite sets: the dissipative dynamics of computing structures</a>,  Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
%H A001765 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=303">Encyclopedia of Combinatorial Structures 303</a>
%F A001765 E.g.f.: -log(1+log(1+log(1+log(1+log(1+log(1+log(1-x))))))).
%t A001765 With[{nn=20},CoefficientList[Series[-Log[1+Log[1+Log[1+Log[1+Log[1+Log[1+Log[1-x]]]]]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 07 2023 *)
%o A001765 (PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, abs(stirling(n, j, 1))*T(j, k-1)));
%o A001765 a(n) = T(n, 7); \\ _Seiichi Manyama_, Feb 11 2022
%o A001765 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-log(1+log(1+log(1+log(1+log(1+log(1+log(1-x))))))))) \\ _Seiichi Manyama_, Feb 11 2022
%Y A001765 Cf. A003713, A000268, A000310, A000359, A000406.
%K A001765 nonn,easy
%O A001765 1,2
%A A001765 _N. J. A. Sloane_