%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 }