Raymond Hettinger added the comment:

I know this was considered at the beginning but I am not immediately 
remembering what the reason was for not doing it (however, I do remember 
looking to APL to see what was done for their well thought-out implementation 
of accumulate).

AFAIK, the case you sketched-out (computing running totals for four factorial 
starting from an initial product of 10) just doesn't come-up in the real-world. 
 I'm reluctant to have API feature-creep without strong use cases (it just 
makes the tool more complicated to learn, remember, and use).  When I get a 
chance, I'll go to github and run a code search to see whether people are 
routinely have to do a chain() operation to prepend a starting point; if it 
isn't rare, then there would be a better case for API expansion; if it is rate, 
then it goes in the it-isn't-worth it category.

----------
priority: normal -> low

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Python tracker <rep...@bugs.python.org>
<http://bugs.python.org/issue25193>
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