On the expansion of the power of any polynomial (1 + x + x2 + x3 + x4 + etc.)n
In this paper, Euler gives: (1) the general trinomial coefficient as a sum of binomial coefficients, (2) the general quadrinomial coefficient as a sum of binomial and trinomial coefficients (3) the general quintonomial coefficient as a sum of binomial and quadrinomial coefficients; and (4) a way to determine the coefficients in any polynomial (1+x+x2 + ... + xm)n as a sum of the coefficients of lower-degree polynomials. (Based on Jordan Bell's translation abstract.)
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 12, pp. 47-57.
Opera Omnia Citation
Series 1, Volume 16B, pp.28-40.