Repeated sequences

[Joshua Zucker]

Calculus-wise, yes, 0^0 is indeterminate.  So if 0^0 is a limit of
some f(x)^g(x), perhaps it could have any value.  But for any
reasonably "nice" f and g except for silly things like the constant f
= 0, it ends up being 1.

Combinatorially, I have seen a lot of places where 0^0 = 1 saves me
from having to introduce a special case into some computation, and
very few if any -- I can't think of any off the top of my head, anyway
-- where 0^0 = 0 or 0^0 = indeterminate would be better.

Since we're talking integer sequences, seems to me that most of the
time 0^0 = 1 would be the more convenient definition to adopt, and
then any seq-contributors who want to have it otherwise can mention it
in their comments, while 0^0 = 1 can go without saying.

--Joshua Zucker