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%I #9 Mar 30 2012 18:39:32
%S 0,1,1,1,1,2,4,8,18,43,107,282,771,2167,6241,18421,55309,168845,
%T 524728,1649764
%N Maximum cardinality of a subset of Dyck n-paths p that share both the same area and the same maj(beta(p)) statistic.
%C The maj(beta(p)) statistic is the major index of the "billiard ball" path under p.
%H Jason Bandlow and Kendra Killpatrick, <a href="http://www.math.upenn.edu/~jbandlow/papers/invq.pdf">An Area-to-Inv Bijection Between Dyck Paths and 312-avoiding Permutations</a>
%e For n=8 there are 18 paths with area = 9 and maj(beta(p)) = 10 (and vice versa). No other conforming subset of Dyck 8-paths has greater cardinality.
%K nonn
%O 0,6
%A _David Scambler_, Jul 31 2011
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