TITLE: Factorial-based constant
QUESTION [7 upvotes]: Am looking for a name for:
$$\prod\dfrac{1}{1-\dfrac{1}{n!}}$$
$$=2.529477472079152648180116154253954242$$
Wolfram|Alpha
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.

REPLY [15 votes]: 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, 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.