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Series expansion of Lambert series


Define for 0<=x<1 the Lambert series

f[x_] := Sum[ x^n/(1-x^n), {x,1,oo}]

How do I get Mathematica to calculate the first few terms of a series
expansion like

Series[f[x],{x,0,4}] ?

Also a series like

e1[x_] := Sum[x^n/(1+n!), {n,0,oo}]

does not seem to be expandable with Series.

BTW same thing in 8.0 and 5.2

Regards,
Wolfgang



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