Expansion of base-e pentation

[andydude]

So I have been revamping the functions I use for tetration, and I recently solved all the mumbo-jumbo to use tetration as the function in the NaturalIterate function. So now you can do:

Code:

<<Tetration`
NaturalIterate[Series[Tetrate[E, x], {x, 0, 3}], z]

I'm still working on doing this for other bases, but this is enough to get an expansion of pentation about zero.

What follows below is InverseSeries[...] of the output from above. In other words, the above gives the coefficients of the base-e penta-logarithm about (0), and the following gives the coefficients of the base-e penta-exponential about (-1).

Code:

0,
0.997386001614238200000,
-0.044854069033065140000,
0.008127184531878105000,
0.045268576293608810000,
-0.009169795166599723000,
0.000529626080101428000,
0.003682350459440369500,
-0.001300714479652927000,
0.000136554270543782140,
0.000349632018705509600,
-0.000212903018660854500,
0.000030850789704285015,
0.000053653522961255240,
-0.000028243223065159680,
-0.000003800898968414997,
0.000000972449120890964,
0.000005775482651540000,
0.000010790317715530437,
-0.000029357772002764790,
0.000020775705975594905

So, what I'm wondering is, how do I turn this into an expansion about 3i?