Could be tetration if this integral converges

[mike3]

WOW, this is easier than I thought...

All we do is take that \( a_n = {^n} e \) and \( c_n = {^n} e \) (there seems to be a mistake as the post as written seems to suggest we should take \( c_n = -{^n} e \) and that doesn't seem to work), and \( z_n = n \) (the indexes at which we are to interpolate), which gives

\( F(z) = \sum_{n=0}^{\infty} e^{({^n} e) (z - n)} ({^n} e) \frac{(-1)^n \sin(\pi z)}{\pi (z - n)} \)

as an entire interpolant for the tetrational sequence.

What are the values for F (0,1,2,3)?

\( ^0 e \), \( ^1 e \), \( ^2 e \), \( ^3 e \), ... .