Hi,

Looking around, it seems Sage does not yet implement harmonic numbers
(except via SymPy)? If anyone is interested, I benchmarked a few
different algorithms and blogged about it here:
http://fredrik-j.blogspot.com/2009/02/how-not-to-compute-harmonic-numbers.html

Besides (generalized) harmonic numbers, there is potential for
asymptotically fast computation of Stirling numbers with large n and
small k. GAP (which Sage uses) takes 3.5 seconds to compute
S1(10000,2) on my system while algorithm #5 from my blog post takes
0.05 seconds.

I'm curious if anyone here knows of faster algorithms for harmonic
numbers / Stirling numbers? This list seems like the right place to
ask :-)

Fredrik

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