most recent 30 from http://mathoverflow.net 2013-05-18T19:15:36Z http://mathoverflow.net/feeds/question/42261 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42261/need-help-condensing-a-binomial-expression Bruce 2010-10-15T08:52:12Z 2010-10-15T08:59:05Z

<p>Here is the expression: </p> <p>(n,1) + (n,2)[2^2 - 1] + (n,3)[2^3 - 1] + ...... (n,k)[2^k - 1] </p> <p>(n,r) = n! / r! * (n-r)!</p> <p>I know when k = n the expression reduces to 3^n - 2^n. I need to find the condensed version of this expression in terms of 'k'. Any help will be appreciated.</p>