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%I #8 Oct 10 2018 02:42:12
%S 1,3,22,292,6120,193594,9070536,622336756,61915861962,8846814822932,
%T 1798543906246948,515674104905890202,206833212761446463192,
%U 115198617558900993580396,88503974769306037986089170,93233054587165663487254293572
%N Number of down-arrow-indecomposable topologies on n labeled points.
%H L. Foissy and C. Malvenuto, <a href="http://arxiv.org/abs/1407.0476">The Hopf algebra of finite topologies and T-partitions</a>, arXiv preprint arXiv:1407.0476, 2014
%F G.f.: (A000798(x)-1)/A000798(x), where A000798(x) is the g.f. of A000798.
%t A000798 = {1, 1, 4, 29, 355, 6942, 209527, 9535241, 642779354, 63260289423, 8977053873043, 1816846038736192, 519355571065774021, 207881393656668953041, 115617051977054267807460, 88736269118586244492485121, 93411113411710039565210494095, 134137950093337880672321868725846, 261492535743634374805066126901117203};
%t f[x_] = Sum[A000798[[n+1]] x^n, {n, 0, nmax = Length[A000798]-1}];
%t CoefficientList[(f[x]-1)/f[x] + O[x]^nmax, x][[2 ;; -2]] (* _Jean-François Alcover_, Oct 10 2018 *)
%Y Cf. A000598, A247660.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Oct 05 2014
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