Closed formula for Dedekind numbers

Determine a closed formula, in terms of the number of players, for the number of monotone Boolean functions with distinguishable variables.

Background

Dedekind’s problem concerns enumerating monotone Boolean functions when the variables are distinguishable, equivalently counting simple games before identifying games under permutations of players. The paper places this problem in the historical context of partial computational and theoretical progress, noting that the ninth Dedekind number was only recently determined. The unresolved objective is a general closed formula depending on the number of variables or players.