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.
%0 Generic
%1 citeulike:3036287
%A Euler, Leonhard
%D 2005
%K Vor1850 available-in-tex-format combinatorics mathematics pre1850
%T On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc
%U http://arxiv.org/abs/math/0505425
%X 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.
@misc{citeulike:3036287,
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.},
added-at = {2009-08-02T17:14:35.000+0200},
archiveprefix = {arXiv},
author = {Euler, Leonhard},
biburl = {https://www.bibsonomy.org/bibtex/23f6405738756a23ed4d3d177695c1e81/rwst},
citeulike-article-id = {3036287},
citeulike-linkout-0 = {http://arxiv.org/abs/math/0505425},
citeulike-linkout-1 = {http://arxiv.org/pdf/math/0505425},
description = {my bookmarks from citeulike},
eprint = {math/0505425},
interhash = {35f6162f70ce2f83f34d9aef749b5007},
intrahash = {3f6405738756a23ed4d3d177695c1e81},
keywords = {Vor1850 available-in-tex-format combinatorics mathematics pre1850},
month = May,
posted-at = {2008-07-23 08:49:49},
priority = {2},
timestamp = {2009-08-06T10:25:55.000+0200},
title = {On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc},
url = {http://arxiv.org/abs/math/0505425},
year = 2005
}