most recent 30 from http://mathoverflow.net 2013-05-24T13:37:57Z http://mathoverflow.net/feeds/question/40803 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40803/how-to-simplify-this-combinatorial-expression Osiris 2010-10-02T00:16:51Z 2010-10-02T00:16:51Z

<p>$f(m,n)=\binom{m}{m}\binom{n}{1}+\binom{m}{m-1}\binom{n}{2}+\cdots+\binom{m}{2}\binom{n}{m-1}+\binom{m}{1}\binom{n}{m}=?$</p> <p>Can we simplify the expression above?</p>