Constructing the "analytical" formula for tetration.

[Gottfried]

News: I may have just found a really complicated but "explicit" or "non-recursive" formula for the solutions of a general recurrence sequence of the form

\( a_1 = r_{1, 1} \),
\( a_n = \sum_{m=1}^{n-1} r_{n, m} a_m \)

which these Schroder function coefficient equations belong to.

It's not "nice", though, but it looks to work (no proof yet as it was found by pattern examination). If you want details, just ask. But at least it seems to show that an explicit formula exists, so that there may perhaps be a simpler, more "elegant" one.

Wow. If this is not uncomfortably much work then show this please. Perhaps it gives a bit more insight into the whole problem as well as into that of my special "hobby", the iterationseries... or at least some fresh idea.

Gottfried