This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001669 M4443 N1879 #46 Feb 01 2022 01:21:37
%S A001669 1,1,7,70,910,14532,274778,5995892,148154860,4085619622,124304629050,
%T A001669 4133867297490,149114120602860,5796433459664946,241482353893283349,
%U A001669 10730629952953517859,506500241174366575122,25302666611855946733140
%N A001669 Number of 7-level labeled rooted trees with n leaves.
%D A001669 J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%D A001669 T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
%D A001669 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001669 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001669 Alois P. Heinz, <a href="/A001669/b001669.txt">Table of n, a(n) for n = 0..150</a>
%H A001669 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 A001669 Jekuthiel Ginsburg, <a href="/A000405/a000405.pdf">Iterated exponentials</a>, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]
%H A001669 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 A001669 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=296">Encyclopedia of Combinatorial Structures 296</a>
%H A001669 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A001669 E.g.f.: exp(exp(exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)-1).
%p A001669 g:= proc(p) local b; b:= proc(n) option remember; if n=0 then 1 else (n-1)! *add(p(k)*b(n-k)/ (k-1)!/ (n-k)!, k=1..n) fi end end: a:= g(g(g(g(g(g(1)))))): seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 11 2008
%t A001669 g[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, (n-1)!*Sum[p[k]*b[n-k]/(k-1)!/(n-k)!, {k, 1, n}]]; b]; a = Nest[g, 1&, 6]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 10 2014, after _Alois P. Heinz_ *)
%t A001669 With[{nn=20},Join[{1},Rest[CoefficientList[Series[Nest[Exp[#]-1&,Exp[x]-1,6],{x,0,nn}],x] Range[0,nn]!]]] (* _Harvey P. Dale_, Mar 02 2015 *)
%Y A001669 Cf. A000110, A000258, A000307, A000357, A000405.
%Y A001669 Column k=6 of A144150.
%K A001669 nonn,easy
%O A001669 0,3
%A A001669 _N. J. A. Sloane_
%E A001669 Extended with new definition by _Christian G. Bower_, Aug 15 1998