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Don:
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For a future AA qual problem
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(1)  Let $S↓{nk}$ be the Stirling number of the First kind.  What is
the asymptotic behavior of $S↓{n,3}$/$S↓{n,1}$?

Answer:
$$\displaylines{{1\over 1\cdot2}+{1\over 1\cdot3}+{1\over 2\cdot3}
+{1\over 1\cdot4}+{1\over 2\cdot4}
+{1\over 3\cdot4}+{1\over 1\cdot5}+\cdots {1\over (n-1)↑n}\cr
\qquad={H↑2↓n - H↑{(2)}↓n \over 2}\approx {\ln n+\gamma )↑2 - {\pi↑2\over 6}\over 2}+
O{(1\over n)}\cr}$$
or

(2)  Express
$$\sum {1\over ijk} [1 ≤ i < j < k ≤ n]$$ 
in terms of Stirling numbers.

Answer: 
$$\displaylines{S↓{n+1,4}$/$(n+1)!}$$
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