Find Nth term of the series 1, 5, 32, 288 …

Given a number n, the task is to find the n-th term in series 1, 5, 32, 288 …

Examples:

Input: N = 3
Output: 32
Explanation:
3rd term = 3^3 + 2^2 + 1^1
= 32

Input: N = 4
Output: 288
Explanation:
4th term = 4^4 + 3^3 + 2^2 + 1^1 
= 288

Approach:

Nth term = n^n + (n-1)^(n-1) + (n-2)^(n-2) + ……..1^1.

Implementation of the above approach is given below:

C++

// CPP code to generate  'Nth' terms
// of this sequence

#include <bits/stdc++.h>
using namespace std;

// Function to generate a fixed \number
int nthTerm(int N)
{
    int nth = 0, i;

    // Finding nth term
    for (i = N; i > 0; i--) {

        nth += pow(i, i);
    }
    return nth;
}

// Driver Method
int main()
{
    int N = 3;
    cout << nthTerm(N) << endl;
    return 0;
}

Java

// Java code to generate 'Nth' terms
// of this sequence
import java.lang.Math;
class GFG {

    // Function to generate a fixed \number
    public static int nthTerm(int N)
    {
        int nth = 0, i;

        // Finding nth term
        for (i = N; i > 0; i--) {

            nth += Math.pow(i, i);
        }
        return nth;
    }

    // Driver Method
    public static void main(String[] args)
    {
        int N = 3;
        System.out.println(nthTerm(N));
    }
}
// This code is contributed by 29AjayKumar

Python3

# Python3 code to generate 'Nth'
# terms of this sequence

# Function to generate a
# fixed number
def nthTerm(N):
    nth = 0

    # Finding nth term
    for i in range(N, 0, -1):
        nth += pow(i, i)
    return nth

# Driver code
N = 3
print(nthTerm(N))

# This code is contributed
# by Shrikant13

C#

// C# code to generate 'Nth' terms
// of this sequence
using System;

class GFG
{

    // Function to generate a fixed \number
    public static int nthTerm(int N)
    {
        int nth = 0, i;

        // Finding nth term
        for (i = N; i > 0; i--)
        {
            nth +=(int)Math.Pow(i, i);
        }
        return nth;
    }

    // Driver Method
    public static void Main()
    {
        int N = 3;
        Console.WriteLine(nthTerm(N));
    }
}

// This code is contributed by Code_Mech.

PHP

<?php
// PHP code to generate 'Nth' terms
// of this sequence

// Function to generate a fixed \number
function nthTerm($N)
{
    $nth = 0; $i;

    // Finding nth term
    for ($i = $N; $i > 0; $i--)
    {

        $nth += pow($i, $i);
    }
    return $nth;
}

// Driver Code
$N = 3;
echo(nthTerm($N));

// This code is contributed by Code_Mech.
?>

Javascript

<script>
// Javascript code to generate  'Nth' terms
// of this sequence

// Function to generate a fixed \number
function nthTerm(N)
{
    let nth = 0, i;

    // Finding nth term
    for (i = N; i > 0; i--)
    {

        nth += Math.pow(i, i);
    }
    return nth;
}

// Driver Method
let N = 3;
document.write(nthTerm(N));

// This code is contributed by subham348.
</script>

Output:

32

Time Complexity: O(NlogN), since there is one loop used and the inbuilt pow function takes O(logN) time.
Auxiliary Space: O(1), since no extra space has been taken.