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falling factorial

Calculates the falling factorial with arguments \e x and \e n.
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Interface

C++
Excel
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Falling Factorial

 
doublefalling_factorialdoublex
intn )
The falling factorial has the following formula

Note that the number of <em> injections </em> or 1-to-1 mappings from a set of n elements to a set of m elements is [m]_n. The number of permutations of n objects out of m is [m]_n. Moreover, the Stirling numbers of the first kind can be used to convert a falling factorial into a polynomial, as follows:

Example:

#include <codecogs/maths/combinatorics/arithmetic/falling_factorial.h>
#include <iostream>
int main()
{
  std::cout << Maths::Combinatorics::Arithmetic::falling_factorial(4, 2) << std::endl;
  return 0;
}

Output:

12

References:

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

Parameters

xthe first falling factorial argument
nthe second falling factorial argument

Returns

the falling factorial of the pair of values x and n

Authors

Lucian Bentea (August 2005)
Source Code

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