[seqfan] A019575 challenge
Charles Greathouse
charles.greathouse at case.edu
Thu Aug 19 22:13:04 CEST 2010
A019575 is:
Place n distinguishable balls in n boxes (in n^n ways); let T(n,k) =
number of ways that max in any box is k, for 1<=k<=n; sequence gives
triangle of numbers T(n,k).
It strikes me as a useful sequence that comes up in many applications.
For example, I recently found someone asking (not in these terms) for
a weighted sum over T(16, k) for the purpose of estimating the number
of cache misses in a GPU.
The formula, as listed, is confusing. Can anyone determine a better
(ideally, an efficient) formula or gf? Also, a b-file might be nice,
though at the moment there's no good way to visualize large triangular
arrays.
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
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