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# bell numbers list

Returns the Bell numbers of order 0 to n.
Controller: CodeCogs   ## Dependents C++

## Bell Numbers List

 std::vectorbell_numbers_list( int n )
The Bell number is defined as the number of partitions (of any size) of a set into n distinguishable objects.

It is also the number of restricted growth functions on . Note that the Stirling numbers of the second kind, , count the number of partitions of n objects into m classes, and so it is true that

For example, there are 15 partitions of a set of 4 objects:

and so . The recurrence relation used with this function to calculate the Bell number of order i is as follows:

where i takes values from 0 to n.

## References:

SUBSET, a C++ library of combinatorial routines, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html

### Example 1

#include <codecogs/maths/combinatorics/sequences/bell_numbers_list.h>
#include <iostream>

int main() {
std::vector<int> result = Maths::Combinatorics::Sequences::bell_numbers_list(5);
std::cout << "Number of values: " << result.size() << std::endl;
for (int i = 0; i < result.size(); i++)
std::cout << result[i] << "  ";
std::cout << std::endl;

return 0;
}
Output
Number of values: 6
1  1  2  5  15  52

### Parameters

 n the maximum value of the index in the generated Bell sequence

### Returns

the Bell numbers of order 0 to n

### Authors

Lucian Bentea (August 2005)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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