Geodesic
A combinatorial interpretation of the numbers \(6(2n)!/n!(n+2)!\)
Journal of integer sequences, Tome 8 (2005) no. 2
It is well known that the numbers $(2m)!(2n)!/m!n!(m+n)$! are integers, but in general there is no known combinatorial interpretation for them. When $m=0$ these numbers are the middle binomial coefficients $C(2n,n)$, and when $m=1$ they are twice the Catalan numbers. In this paper, we give combinatorial interpretations for these numbers when $m=2$ or 3.
Classification : 05A10, 05A15
Keywords: Dyck paths, super Catalan numbers (Concerned with sequences and 
@article{JIS_2005__8_2_a2,
     author = {Gessel,  Ira M. and Xin,  Guoce},
     title = {A combinatorial interpretation of the numbers \(6(2n)!/n!(n+2)!\)},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {2},
     zbl = {1064.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a2/}
}
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Gessel,  Ira M.; Xin,  Guoce. A combinatorial interpretation of the numbers \(6(2n)!/n!(n+2)!\). Journal of integer sequences, Tome 8 (2005) no. 2. http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a2/