Babai, L. and Lengyel, T. "A Convergence Criterion for Recurrent Sequences with Application to the Partition Lattice." Analysis12,
109-119, 1992.Finch, S. R. "Lengyel's Constant." §5.7
in Mathematical
Constants. Cambridge, England: Cambridge University Press, pp. 316-321,
2003.Flajolet, P. and Salvy, B. "Hierarchal Set Partitions and
Analytic Iterates of the Exponential Function." Unpublished manuscript, 1990.Lengyel,
T. "On a Recurrence Involving Stirling Numbers." Europ. J. Comb.5,
313-321, 1984.Sloane, N. J. A. Sequences A005121/M3649
and A086053 in "The On-Line Encyclopedia
of Integer Sequences."
denote the partition lattice of the set 
. The maximum element
of 
is
denote the number of chains of any length in 
containing both 
and 
. Then 
satisfies the recurrence
relation
and 
is a Stirling number of the second
kind. The first few values of 
for 
, 2, ... are then 1, 1, 4, 32, 436, 9012, 262760, ... (OEIS
A005121).
, and Flajolet and Salvy (1990) improved the result
of Babai and Lengyel (1992) to show that
