bell numbers list

Dependents

this module uses 3 subunits binomial_coefficient_gammaLog_GammaMachine_Epsilon

Interface

Bell Numbers List

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.

Not a member, then Register with CodeCogs. Already a Member, then Login.