E709  De evolutione potestatis polynomialis cuiuscunque (1 + x + x^{2} + x^{3} + x^{4} + etc.)^{n}
(On the expansion of the power of any polynomial 1 + x + x^{2} + x^{3} + x^{4} + etc.)
Summary:
(based on Jordan Bell's abstract)
In this paper, Euler gives
 the general trinomial coefficient as a sum of binomial coefficients,
 the general quadrinomial coefficient as a sum of binomial and trinomial coefficients,
 the general quintonomial coefficient as a sum of binomial and quadrinomial coefficients, and
 a way to determine the coefficients in any polynomial (1 + x + x^{2} + ... + x^{m})^{n}
as a sum of the coefficients of lowerdegree polynomials.
Publication:

Originally published in Nova Acta Academiae Scientarum Imperialis Petropolitinae 12, 1801, pp. 4757

Opera Omnia: Series 1, Volume 16, pp. 28  40
Documents Available:
 Original Publication: E709
 English translation (Jordan Bell): E709
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