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%I #24 Oct 30 2013 19:41:08
%S 1,1,2,5,12,30,80,219,614,1766,5206,15646,47834,148602,468110,1492841,
%T 4814682,15686156,51575438
%N Number of Dyck paths of semilength n for which the multiset of ascent lengths and the multiset of descent lengths are the same partition of n.
%e For n=4 the paths UUUDDUDD and UUDUUDDD fail the definition because {2,2} != {3,1} so a(4) = 12 rather than Catalan(4)=14.
%K nonn,more
%O 0,3
%A _David Scambler_, Jan 08 2011
%E a(15)-a(18) from _Alois P. Heinz_, May 07 2012
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