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A179544
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.
0
1, 1, 2, 5, 12, 30, 80, 219, 614, 1766, 5206, 15646, 47834, 148602, 468110, 1492841, 4814682, 15686156, 51575438
OFFSET
0,3
EXAMPLE
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.
CROSSREFS
Sequence in context: A363306 A003089 A213263 * A182488 A363912 A261788
KEYWORD
nonn,more
AUTHOR
David Scambler, Jan 08 2011
EXTENSIONS
a(15)-a(18) from Alois P. Heinz, May 07 2012
STATUS
approved