A proof of Julian West's conjecture that the number of two-stacksortable permutations of length n is 2(3n)!/((n + 1)!(2n + 1)!)

Zeilberger, D., A proof of Julian West’s conjecture that the number of two-stack-sortable permutations of length n is 2(3n)!/((n + 1)!(2n + l)!), Discrete Mathematics 102 (1992) 85-93. The Polya-Schutzenberger-Tutte methodology of weight enumeration, combined with about 10 hours of CPU time (of Maple running on Drexel University’s Sun network) established Julian West’s conjecture that 2-stack-sortable permutations are enumerated by sequence #651 in the Sloane listing.