Bell NumbersDate: 10/15/98 at 11:50:20 From: John Leonardi Subject: Bell Numbers I am doing math research on Bell Numbers. I have two questions. How are Bell numbers generated? The other question I have is what are the first twelve Bell numbers? Date: 10/16/98 at 08:17:03 From: Doctor Rob Subject: Re: Bell Numbers The Bell numbers count the number of ways to partition a set of n elements into subsets. One way to generate them is: b(0) = 1 b(n) = Sum C(n-1,k)*b(k), 0 <= k <= n-1 where C(a,b) = a!/(b!*[a-b]!) are binomial coefficients. They begin: 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 2764437, 190899322, 1382958545, 10480142147, 828648699804, ... - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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