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?
Is this identity involving Stirling numbers of the first kind well-known?
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combinatorics
reference-request
stirling-numbers
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0It'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. – 2011-03-02
1 Answers
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The identity and the proof for the identity are there in the wiki link you have sent.
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1Also noted at [OEIS A001303](http://oeis.org/A001303) which has other formulae and several references to the sequence – 2011-03-02