We count the number of partitions of a set of elements, depending on the size of the block containing the st element. If the block has size for then we have choices for the other elements of the block. The remaining elements can be partitioned in ways. We have therefore that:
Using the formula above, one can easily derive the first few Bell numbers. Starting with , the first ten Bell numbers are 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147.
|Date of creation||2013-03-22 14:47:07|
|Last modified on||2013-03-22 14:47:07|
|Last modified by||aoh45 (5079)|