*I've asked that question before on History of Science and Mathematics but haven't received an answer*

Does someone have a reference or further explanation on Gauß' entry from May 24, 1796 in his mathematical diary (Mathematisches Tagebuch, full scan available via https://gdz.sub.uni-goettingen.de/id/DE-611-HS-3382323) on page 3 regarding the divergent series $$1-2+8-64...$$ in relation to the continued fraction $$\frac{1}{\displaystyle 1+\frac{\strut 2}{\displaystyle 1+\frac{\strut 2}{\displaystyle 1+\frac{\strut 8}{\displaystyle 1+\frac{\strut 12}{\displaystyle 1+\frac{\strut 32}{\displaystyle 1+\frac{\strut 56}{\displaystyle 1+128}}}}}}}$$

He states also - if I read it correctly - *Transformatio seriei* which could mean *series transformation*, but I don't see how he transforms from the series to the continued fraction resp. which transformation or rule he applied.

The OEIS has an entry (https://oeis.org/A014236) for the sequence $2,2,8,12,32,56,128$, but I don't see the connection either.

My question: Can anyone help or clarify the relationship that Gauss' used?

Torsten Schoeneberg remarked rightfully in the original question that the term in the series are $(-1)^n\cdot 2^{\frac{1}{2}n(n+1)}$ and Gerald Edgar conjectures it might be related to Gauss' Continued Fraction.