Is $\frac{(3n)!}{n!(n+1)!(n+2)!}$ integer for any integer $n \ge 3$?

Asked Jan 08 '20 at 21:22

Active Jan 08 '20 at 21:22

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Inspired by this question and its comments, I suspect that:

$$\frac{(3n)!}{n!(n+1)!(n+2)!}$$

is integer for any integer $n \ge 3$, because I have run this at WolframAlpha.

I tried some binomial coefficient manipulation, like in the linked question, without success.

Any idea?

asked Jan 08 '20 at 21:22

Fabius Wiesner

2

Searching with Approach0 returns some posts on AoPS on this topic: https://artofproblemsolving.com/community/c6h1573703p9677208 https://artofproblemsolving.com/community/c4h1236440p6286381 – Martin Sleziak Jan 08 '20 at 21:28
1

Thank you @Martin Sleziak. It turned out that one possible answer is already in math.stackexchange here. – Fabius Wiesner Jan 08 '20 at 21:42

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