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# Euler Triangle Row

Computes the row of order \e n in the Euler triangle.
Controller: CodeCogs   C++

## Euler Triangle Row

 std::vectoreuler_triangle_row( int n )
The value in the n-th row and k-th column of the Euler triangular matrix equals the number of permutations of the n digits that have exactly k <em> ascents </em>, that is, k places where the i-th digit is less than the <em>(i+1)</em>-th digit.

## Example:

```#include <codecogs/maths/combinatorics/sequences/euler_triangle_row.h>
#include <iostream>
int main() {
std::vector<int> row = Maths::Combinatorics::Sequences::euler_triangle_row(9);
std::cout << "Size of row: " << row.size() << std::endl;
for (int i = 0; i < row.size(); i++)
std::cout << row[i] << "  ";
std::cout << std::endl;
return 0;
}```

## Output:

```Size of row: 9
1  502  14608  88234  156190  88234  14608  502  1```

## References:

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

### Returns

the entries of the row in Euler triangle

### 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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