Geodesic
A combinatorial interpretation of the numbers $6(2n)!/n!(n+2)!$
Journal of integer sequences, Tome 8 (2005) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a2/}
}
TY  - JOUR
AU  - Gessel, Ira M.
AU  - Xin, Guoce
TI  - A combinatorial interpretation of the numbers $6(2n)!/n!(n+2)!$
JO  - Journal of integer sequences
PY  - 2005
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a2/
LA  - en
ID  - JIS_2005__8_2_a2
ER  - 
%0 Journal Article
%A Gessel, Ira M.
%A Xin, Guoce
%T A combinatorial interpretation of the numbers $6(2n)!/n!(n+2)!$
%J Journal of integer sequences
%D 2005
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a2/
%G en
%F JIS_2005__8_2_a2
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/