# Second-order Eulerian numbers

Last Updated : 28 Feb, 2023

The d-order Eulerian numbers series can be represented as

1, 0, 0, 2, 8, 22, 52, 114, 240, 494, 1004, …..

Nth term

Given an integer N. The task is to find the N-th term of the given series.
Examples

Input: N = 0
Output:
term = 1
Input: N = 4
Output:

Approach: The idea is to find the general term for the Second-order Eulerian numbers. Below is the computation of the general term for second-order eulerian numbers:

0th term = 20 – 2*0 = 1
1st Term = 21 – 2*1 = 0
2nd term = 22 – 2*2 = 0
3rd term = 23 – 2*3 = 2
4th term = 24 – 2*4 = 8
5th term = 25 – 2*5 = 22

Nth term = 2n – 2*n.
Therefore, the Nth term of the series is given as

Below is the implementation of above approach:

## C++

 `// C++ implementation to ``// find N-th term in the series` `#include ``#include ``using` `namespace` `std;` `// Function to find N-th term``// in the series``void` `findNthTerm(``int` `n)``{``    ``cout << ``pow``(2, n) - 2 * n << endl;``}` `// Driver Code``int` `main()``{``    ``int` `N = 4;``    ``findNthTerm(N);` `    ``return` `0;``}`

## Java

 `// Java implementation to find ``// N-th term in the series ``class` `GFG{ ` `// Function to find N-th term``// in the series``static` `void` `findNthTerm(``int` `n)``{``    ``System.out.println(Math.pow(``2``, n) - ``2` `* n);``}` `// Driver code ``public` `static` `void` `main(String[] args) ``{ ``    ``int` `N = ``4``;``    ``findNthTerm(N);``} ``} ` `// This code is contributed by Pratima Pandey `

## Python3

 `# Python3 implementation to ``# find N-th term in the series` `# Function to find N-th term``# in the series``def` `findNthTerm(n):` `    ``print``(``pow``(``2``, n) ``-` `2` `*` `n);` `# Driver Code``N ``=` `4``;``findNthTerm(N);` `# This code is contributed by Code_Mech`

## C#

 `// C# implementation to find ``// N-th term in the series ``using` `System;``class` `GFG{ ` `// Function to find N-th term``// in the series``static` `void` `findNthTerm(``int` `n)``{``    ``Console.Write(Math.Pow(2, n) - 2 * n);``}` `// Driver code ``public` `static` `void` `Main() ``{ ``    ``int` `N = 4;``    ``findNthTerm(N);``} ``} ` `// This code is contributed by Code_Mech`

## Javascript

 ``

Output:
`8`

The time complexity to compute the second-order Eulerian numbers using this recurrence relation is O(n^2), where n is the maximum value of n or m. This is because we need to compute each value of A(n, m) by recursively computing A(n-1, m) and A(n-1, m-1) until we reach the base case A(0, 0) = 1.

Reference:OEIS