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A Combinatorial Interpretation of the Numbers 6(2n)!/n!(n+2)!
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Ira M. Gessel and Guoce Xin

Department of Mathematics

Brandeis University

Waltham, MA 02454-9110

USA

**Abstract:**
It is well known that the numbers
(2*m*)!(2*n*)!/*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(2*n*,*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.

(Concerned with sequences
A007054 and
A007272
.)

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Received March 5 2005;
revised version received March 16 2005.
Published in *Journal of Integer Sequences* April 27 2005.

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