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Rising Factorial

Calculates the rising factorial with arguments \e x and \e n.
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C++
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Rising Factorial

 
doublerising_factorialdoublex
intn )
The rising factorial has the following formula

Note that the number of ways of arranging n objects in m ordered boxes is [m]^n. (Here, the ordering in each box matters). Thus, 2 objects in 2 boxes have the following 6 possible arrangements:

Moreover, the number of non-decreasing maps from a set of n to a set of m ordered elements is [m]^n / n!. Thus the set of nondecreasing maps from (1,2,3) to (a,b,c,d) is the 20 elements:

Example:

#include <codecogs/maths/discrete/combinatorics/arithmetic/rising_factorial.h>
#include <iostream>
int main()
{
  std::cout << Maths::Combinatorics::Arithmetic::rising_factorial(5, 3) << std::endl;
  return 0;
}

Output:

210

References:

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

Parameters

xthe first rising factorial argument
nthe second falling factorial argument

Returns

the rising factorial of the pair of values x and 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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