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%I #21 Dec 05 2019 07:08:33
%S 1,1,1,0,1,2,7,27,126,664,3954,26190,190754,1514332,12998035,
%T 119803771,1178740932,12316480222,136060611189,1582930919092,
%U 19328253734491
%N Vertically indecomposable lattices on n unlabeled nodes.
%D J. Heitzig and J. Reinhold, Counting finite lattices, Algebra Universalis, 48 (2002), 43-53.
%H V. Gebhardt and S. Tawn, <a href="http://arxiv.org/abs/1609.08255">Constructing unlabelled lattices</a>, arXiv:1609.08255 [math.CO], 2016.
%H J. Heitzig and J. Reinhold, <a href="http://www-ifm.math.uni-hannover.de/forschung/preprintsifm.html">Counting finite lattices</a>, preprint no. 298, Institut für Mathematik, Universität Hannover, Germany, 1999.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%t A006966 = Cases[Import["https://oeis.org/A006966/b006966.txt", "Table"], {_, _}][[All, 2]];
%t nmax = Length[A006966] - 1;
%t B[x_] = Sum[A006966[[n + 1]] x^n, {n, 0, nmax}];
%t A[x_] = Sum[c[n] x^n, {n, 0, nmax}];
%t sol = CoefficientList[1 + A[x] - 1/(1 - B[x]) + O[x]^nmax, x] == 0 // Solve // First // Rest // Quiet;
%t a[n_] := If[n <= 2, 1, c[n - 2] /. sol];
%t a /@ Range[0, nmax] (* _Jean-François Alcover_, Dec 05 2019 *)
%Y a(n+1) is Inverse INVERT transform of A006966(n+1).
%K nonn,hard,more
%O 0,6
%A _Christian G. Bower_, Dec 28 2000
%E a(19) (computed by Jipsen and Lawless) and a(20) from _Volker Gebhardt_, Sep 28 2016
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