# Is this identity involving Stirling numbers of the first kind well-known?

I've been looking in vain (most books I came across give identities involving sums or recurrence relations, but do not give much attention to fixed values) for a reference to the following identity: $$S(n,n-3)={n \choose 2}{n \choose 4},$$ where $S(n,k)$ is the unsigned Stirling number of the first kind. Is this well-known, or too trivial to be mentioned anywhere?

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It's not trivial, but the constant, 3, is just big enough not to be important enough to be even an exercise in a text. But it's perfect for OEIS as noted below. – Mitch Mar 2 '11 at 13:53

## 1 Answer

The identity and the proof for the identity are there in the wiki link you have sent.

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Oh hell, so much for being careful. I must have missed it the last time I actually visited the page. Thanks. – Anthony Labarre Mar 2 '11 at 9:18
Also noted at OEIS A001303 which has other formulae and several references to the sequence – Henry Mar 2 '11 at 10:46