% A plot of the number of topological spaces of n points in logarithmic scale
% Copyright Pablo (C) 2023
\begin{tikzpicture}
  \begin{axis}[
      xlabel={$n$},
      ylabel={$\log(\text{\# topological spaces of $n$ points})$},
      xmin=0, xmax=20,
      ymin=0, ymax=85,
      legend pos=north west,
      ymajorgrids=true,
      grid style=dashed,
      title={Finite Topological Spaces},
    ]

    \addplot[ycomb, mark=*, color=blue]
    coordinates {
      (1, 0.0) (2, 0.0) (3, 1.3862943611198906)
      (4, 3.367295829986474) (5, 5.872117789475416)
      (6, 8.845345196421732) (7, 12.25260788832186)
      (8, 16.070505071998763) (9, 20.2813120724568)
      (10, 24.870523629947815) (11, 29.825692867915237)
      (12, 35.135878446962565) (13, 40.79136515152374)
      (14, 46.783499368150814) (15, 53.10457040668696)
      (16, 59.74771093408638) (17, 66.70680783627301)
      (18, 73.97642153853138) (19, 81.5517138078997)
    };
  \end{axis}
\end{tikzpicture}