My favorite integer sequence

[Gottfried]

I'll also be much interested if I can learn about the approach how to determine the function f(x) which prognoses/approximates the elements of the sequence. I could implement the function f(x) in Pari/Gp but just did not get the clue how one would arrive at it.
Gottfried

Deriving the continuous function is actually pretty straightforward. I'll use exp(x) as an example:

(...)

By induction:
\(
b_k = \frac{1}{2^{(k-1)k/2} k!}
\)

Then, as I posted previously:

\(
f(x) = \sum_{k=0}^{\infty}\frac{1}{2^{k(k-1)/2} k!} x^k
\)

Ahh, that's very straightforward and very nice. I'll have to contemplate this a while until I can handle this smoothly myself. Thank you so far!

Gottfried