Some of you may want to know about this question:

http://stackoverflow.com/questions/25570037/best-language-to-do-some-annoying-generating-function-computations

excerpt:

The computation relies on a few ingredients.

   1. The first is that I need to be able to compute characters of the 
   symmetric group in an efficient manner.
   2. The next thing is that I need to arrange these into a generating 
   function. This will end up being a generating function in many, many 
   variables, although it will be truncated to a finite degree.
   3. Finally, I need to take the formal logarithm (which will be a 
   generating function in the same number of variables, of the same degree) of 
   this and to extract a specific coefficient.

I have coded this before in Maple, but I don't have access to Maple any 
more. I was thinking of doing so in Sage, but step 1 seems not to be well 
implemented (although there is a workaround, but it doesn't seem to be very 
efficient). Furthermore, I'm pretty sure that while steps 2 and 3 are fine 
in principle, they are very, very slow in Sage.

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