Rational sums of inverse powers of fixed points of e

[Gottfried]

The first one looks about right, meaning it looks familiar at a glance.

Ahh, just I got it myself. I got for the first few approximations (upscaled by factorials)

Code:

-1
          -1
           2
           9
          -6
        -155
        -232
        3969
       20870
     -118779
    -1655028

so I have it now. But for the first n=96 entries I needed ~120 secs, using also only 96 fixpoints (Eulersumming them).
Gottfried