Bell Numbers

Date: 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/