On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc

Leonhard Euler

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On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc

Leonhard Euler

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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+x^2+...+x^m)^n as a sum of the coefficients of lower degree polynomial coefficients.

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BibTeX RIS

Leonhard Euler. 2005-05-20. On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc. https://arxiv.org/abs/math/0505425

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