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MATHEMATICA
| a[x_, n_] := Sum[c[k] x^k, {k, 0, n}] ;
f[x_, n_] := Series[Exp[x] - 1, {x, 0, n}] // Normal;
b[x_, n_] := Series[a[a[x, n], n], {x, 0, n}] // Normal;
eq[n_] := Thread[CoefficientList[f[x, n] - b[x, n], x] == 0] // Rest;
c[0] = 0; so[3] = Solve[eq[3], {c[1], c[2], c[3]}] // First;
so[n_] := so[n] = Solve[eq[n] /. Flatten[Table[so[k], {k, 3, n - 1}]], c[n]] // First
Array[c, 19, 0] /. Flatten[Table[so[k], {k, 3, 19}]] // Denominator
(* From Jean-François Alcover, Jun 8 2011 *)
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