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Thanks for the response! Actually, part of my problem (which I forgot to state above) is how to represent the infinite product. To be honest, I've used Sage for about a year, but have not programmed more than a one-line function. So most of the use has been extremely rudimentary. Is there a way to represent an infinite product? Naively, I expected something like

prod(P(t,k) for k >= 1) == sum(a(k)*t^k for k >= 0)

and then be able to read off the a(k) somehow.