Funny method of extending tetration?

[Gottfried]

offset so it equals 1 at 0). Now, what does

\( \lim_{k \rightarrow \infty} \mathrm{reg}_{\mathrm{RFP}}[e_{2k+1}^x](1) \)

do?

Hi Mike -

Hmm I tried with n=5,n=17,n=27 and got the according Bell-matrices.
Using integer heights iteration worked as expected.
I tried fractional heights, h=0.5,h=0.25 at x=0 and x=1 and the series with truncation at 64 coefficients do not converge well, not even having alternating signs.
So I couldn't discern any interesting result so far... Would you mind to give some more hint?

Gottfried