Abstract
We obtain an explicit formula in terms of the partitions of the positive integer n to express the nth coefficient of the formal series expansion of the reciprocal of a given function. A brief survey shows that our arithmetic proof differs from others, some obtained already in the XIX century. Examples are given to establish explicit formulas for Bernoulli, Euler, and Fibonacci numbers.
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Fera, G., Talamini, V. Reciprocal Function Series Coefficients with Integer Partitions. Mediterr. J. Math. 15, 29 (2018). https://doi.org/10.1007/s00009-018-1076-1
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DOI: https://doi.org/10.1007/s00009-018-1076-1