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We find general solutions to the generating-function equation sum c_q^{(X)}z^q = F(z)^X, where X is a complex number and F(z) is a convergent power serieswith |F(0)| >0. We then use these results to derive finite expressionscontaining only integers or simple fractions for partition functions and forEuler, Bernoulli, and Stirling numbers.

Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers