n! / n^n

[rlahaye at new.rr.com]

There are a number of sequences in the OEIS that are related to Stirling's approximation for the factorial function.  Among them A055775 gives the floor of n^n/n! and A073225 gives the ceiling.  As the subject line of this e-mail indicates, I'm interested in the sum of n!/n^n, i.e. Sum[n=1 to infinity, n!/n^n].  I *believe* this converges to very roughly 1.879853...If so, is it at all interesting...?  And if it is, perhaps it's decimal expansion could be considered for addition to the OEIS ala pi, e etc...?  From Stirling it should approximate to (sqrt(2*pi*n))/e^n.  I realize there is probably nothing of interest here, but am just curious.

Ross