the large number of terms in the summation. Asymptotics The logarithm of the Dedekind numbers can be estimated accurately via the bounds Here the left inequality counts the number of antichains in which each set has exactly elements, and the right inequality was proven by . provided the even more accurate estimates for even n, and for odd n, where and The main idea behind these estimates is that, in most antichains, all the sets have sizes that are very close to n/2. For n = 2, 4, 6, 8 Korshunov's formula provides an estimate that is inaccurate by a factor of 9.8%, 10.2%, 4.1%, and -3.3%, respectively. Notes References . . . As cited by . . . . . . . . . Integer sequences Enumerative combinatorics Mathematical logic Lattice theory Families of sets