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Jul 27, 2011 at 22:51 comment added StevenJ Oh, and also, if $P_T(C)$ was a hypergeometric function then it's easy to add factors of 1/n! into the denominator of the coefficients. I don't know if that suggests that $P_T$ is not a hypergeometric function because if it was then it would be simple to work backwards and express the $b_n$ series in terms of factorials. It seems like if the nth term in that series could be expressed simply someone would have found the expression by now...
Jul 27, 2011 at 22:06 comment added StevenJ I suppose the question then is, what's the nth coefficient in the expansion of the function P_T(C) you have above? Is there a general relationship between the ordinary and exponential generating functions? It seems like there should/might be but I don't know what it is.
Jul 26, 2011 at 19:11 history answered Gerald Edgar CC BY-SA 3.0