A Combinatorial Interpretation of The Numbers $6(2n)! /n! (n+2)!$

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 $(\binom{2 n}{n})$ , 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.

A Combinatorial Interpretation of The Numbers $6 (2 n)! / n! (n + 2)!$

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A Combinatorial Interpretation of The Numbers $6 (2 n)! / n! (n + 2)!$

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A Combinatorial Interpretation of The Numbers 6(2n)!/n!(n+2)!6(2n)!/n!(n+2)!

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A Combinatorial Interpretation of The Numbers 6(2n)!/n!(n+2)!6(2n)!/n!(n+2)!

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A Combinatorial Interpretation of The Numbers $6 (2 n)! / n! (n + 2)!$

讲解博客

AI智能校验

A Combinatorial Interpretation of The Numbers $6 (2 n)! / n! (n + 2)!$

讲解博客

AI智能校验