On the expansion of the power of any polynomial 1+x+x2+x3+x4+etc
Abstract
In this paper, Euler gives the general trionomial coefficient as a sum of the binomial coefficients, the general quadrinomial coefficient as a sum of the binomial and trinomial coefficients, the general quintonomial coefficient as a sum of the binomial and quadrinomial coefficients, and gives a general determination of the coefficients of the expansion of any polynomial (1+x+x2+...+xm)n as a sum of the coefficients of lower degree polynomial coefficients.
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