Am looking for a name for:


$$\prod\dfrac{1}{1-\dfrac{1}{n!}}$$


$$=2.529477472079152648180116154253954242$$


[Wolfram|Alpha](http://www.wolframalpha.com/input/?i=product%20%28n%21%29%2F%28n%21-1%29)


Expanding the formula gives:


$$(1+\frac{1}{2!}+\frac{1}{2!^2}+\dots)(1+\frac{1}{3!}+\frac{1}{3!^2}+\dots)(1+\frac{1}{4!}+\frac{1}{4!^2}+\dots)\dots$$


which gives the possible denominators used in multinomials.



Factorial-based constant
I don't know about a name, but it does have a history. Knopfmacher, Odlyzko, Pittel, Richmond, Stark [D., not H.], Szekeres, and Wormald, The asymptotic number of set partitions with unequal block sizes, available [here](http://www.kurims.kyoto-u.ac.jp/EMIS/journals/EJC/Volume_6/PDF/v6i1r2.pdf), find that it is the residue at $z=1$ of a generating function $$G(z)=\prod\_{k=1}^{\infty}\left(1-{z^k\over k!}\right)^{-1}$$ They relate it to evaluation of sums of multinomial coefficients, and they reference page 126 of Comtet, Advanced Combinatorics. 


