I was disappointed by the output of this:
ContinuedFractionK[1, 1/n, {n, 1, \[Infinity]}] // N
Yes. The formula is equivalent to a continued fraction expansion of Wallis's formula that I believe is due to Stern (Google is not helping me confirm that at the moment). The convergents may be found here:
See the last remark under "Formula" at the OEIS links to see your CF formula.
