p = 0.4;
Table[
  ListPlot[
    Table[{k, Binomial[n, k] (p)^k (1 - p)^(n - k)}, {k, -2, n + 2}],
    Filling -> Axis, 
    PlotRange -> {{n p - 5 Sqrt[n p(1 - p)], n p + 5 Sqrt[n p(1 - p)]},
                  {0, 1.02/Sqrt[2 \[Pi] n p(1 - p)]}},
    Frame -> True,
    Axes -> False,
    FrameTicks -> None,
    PlotStyle -> PointSize[0.02], 
    LabelStyle -> Directive[Larger], 
    FillingStyle -> Directive[Hue[0.6], Thickness[0.01], Opacity[0.3]], 
    ImageSize -> 250, 
    Epilog -> Inset[
      Style["\!\(\*StyleBox[\"n\",\nFontSlant->\"Italic\"]\) = " <> ToString[n], 16],
      {n p + 3.5 Sqrt[n p(1 - p)], 0.8/Sqrt[2 \[Pi] n p(1 - p)]}
      ] 
    ],
  {n, {4, 8, 16, 32, 64, 128, 256, 512}}
  ]
Export["c:/users/stpasha/documents/de_moivre-laplace.gif", %, 
 "DisplayDurations" -> {.5, .5, .5, .5, .5, .5, .5, .25}, 
 "TransparentColor" -> white]

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