Find Nth term of series 1, 4, 15, 72, 420…

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Given a number N. The task is to write a program to find the N^th term in the below series:

1, 4, 15, 72, 420…

Examples:

Input: 3
Output: 15
Explanation: For N = 3, we know that the factorial of 3 is 6 Nth term = 6*(3+2)/2

Input: 6
Output: 2880
Explanation: For N = 6, we know that the factorial of 6 is 720 Nth term = 620*(6+2)/2 = 2880

The idea is to first find the factorial of the given number N, that is N!. Now the N-th term in the above series will be:

N-th term = N! * (N + 2)/2

Below is the implementation of the above approach:

C++

// CPP program to find N-th term of the series: 
// 1, 4, 15, 72, 420… 
#include <iostream> 
using namespace std; 
 
// Function to find factorial of N 
int factorial(int N) 
{ 
    int fact = 1; 
 
    for (int i = 1; i <= N; i++) 
        fact = fact * i; 
         
    // return factorial of N         
    return fact; 
} 
 
// calculate Nth term of series 
int nthTerm(int N) 
{ 
    return (factorial(N) * (N + 2) / 2); 
} 
 
// Driver Function 
int main() 
{ 
    int N = 6; 
     
    cout << nthTerm(N); 
     
    return 0; 
} 

Java

// Java program to find N-th 
// term of the series: 
// 1, 4, 15, 72, 420 
import java.util.*; 
import java.lang.*; 
import java.io.*; 
 
class GFG 
{ 
     
// Function to find factorial of N 
static int factorial(int N) 
{ 
    int fact = 1; 
 
    for (int i = 1; i <= N; i++) 
        fact = fact * i; 
         
    // return factorial of N     
    return fact; 
} 
 
// calculate Nth term of series 
static int nthTerm(int N) 
{ 
    return (factorial(N) * (N + 2) / 2); 
} 
 
// Driver Code 
public static void main(String args[]) 
{ 
    int N = 6; 
     
    System.out.println(nthTerm(N)); 
} 
} 
 
// This code is contributed by Subhadeep 

Python3

# Python 3 program to find 
# N-th term of the series: 
# 1, 4, 15, 72, 420… 
 
# Function for finding 
# factorial of N 
def factorial(N) :
    fact = 1
    for i in range(1, N + 1) :
        fact = fact * i
 
    # return factorial of N 
    return fact
 
# Function for calculating
# Nth term of series
def nthTerm(N) :
 
    # return nth term
    return (factorial(N) * (N + 2) // 2)
 
# Driver code
if __name__ == "__main__" :
     
    N = 6
 
    # Function Calling
    print(nthTerm(N))
 
# This code is contributed
# by ANKITRAI1 

C#

// C# program to find N-th 
// term of the series: 
// 1, 4, 15, 72, 420 
using System; 
 
class GFG 
{ 
     
// Function to find factorial of N 
static int factorial(int N) 
{ 
    int fact = 1; 
 
    for (int i = 1; i <= N; i++) 
        fact = fact * i; 
         
    // return factorial of N     
    return fact; 
} 
 
// calculate Nth term of series 
static int nthTerm(int N) 
{ 
    return (factorial(N) * (N + 2) / 2); 
} 
 
// Driver Code 
public static void Main() 
{ 
    int N = 6; 
     
    Console.Write(nthTerm(N)); 
} 
} 
 
// This code is contributed by ChitraNayal 

PHP

<?php
// PHP program to find 
// N-th term of the series: 
// 1, 4, 15, 72, 420… 
 
// Function for finding 
// factorial of N 
function factorial($N)
{
    $fact = 1;
    for($i = 1; $i <= $N; $i++)
        $fact = $fact * $i;
 
    // return factorial of N 
    return $fact;
}
 
// Function for calculating
// Nth term of series
function nthTerm($N)
{
 
    // return nth term
    return (factorial($N) * 
           ($N + 2) / 2);
}
 
// Driver code
$N = 6;
 
// Function Calling
echo nthTerm($N);
 
// This code is contributed
// by mits
?>

Javascript

<script>
 
// JavaScript program to find N-th term of the series: 
// 1, 4, 15, 72, 420… 
 
// Function to find factorial of N 
function factorial( N) 
{ 
    let fact = 1; 
 
    for (let i = 1; i <= N; i++) 
        fact = fact * i; 
         
    // return factorial of N         
    return fact; 
} 
 
// calculate Nth term of series 
function nthTerm(N) 
{ 
    return (factorial(N) * (N + 2) / 2); 
} 
// Driver code
 
    let N = 6;
   document.write( nthTerm(N) );
 
// This code contributed by aashish1995 
 
</script>

Output

Time Complexity: O(n)
Auxiliary Space: O(1)

Another approach :(Using recursion)

C++

// CPP program to find N-th term of the series:
// 1, 4, 15, 72, 420… 
// Using recursion
#include <iostream>
using namespace std;
 
// Function to find factorial of N
// with recursion 
int factorial(int N)
{
    // base condition
    if( N == 0 || N == 1 )
        return 1; 
    // use recursion 
    return N * factorial( N - 1 );
}
 
// calculate Nth term of series
int nthTerm(int N)
{
    return (factorial(N) * (N + 2) / 2);
}
 
// Driver Function
int main()
{
    int N = 6;
     
    cout << nthTerm(N);
     
    return 0;
}

Java

// Java program to find N-th 
// term of the series:
// 1, 4, 15, 72, 420
import java.util.*;
import java.lang.*;
import java.io.*;
 
class GFG
{
     
// Function to find factorial of N
static int factorial(int N)
{
    // base condition
    if( N == 0 || N == 1 )
        return 1; 
    // use recursion 
    return N * factorial( N - 1 );
}
 
// calculate Nth term of series
static int nthTerm(int N)
{
    return (factorial(N) * (N + 2) / 2);
}
 
// Driver Code
public static void main(String args[])
{
    int N = 6;
     
    System.out.println(nthTerm(N));
}
}

Python3

# Python3 program to find 
# N-th term of the series: 
# 1, 4, 15, 72, 420… 
# Using recursion 
 
# Function to find factorial 
# of N with recursion
def factorial(N):
 
    # base condition 
    if N == 0 or N == 1:
        return 1
 
    # use recursion
    return N * factorial(N - 1)
 
def nthTerm(N):
     
    # calculate Nth term of series
    return (factorial(N) * (N + 2) // 2)
 
# Driver code
N = 6
print(nthTerm(N))
 
# This code is contributed 
# by Shrikant13

C#

// C# program to find N-th 
// term of the series:
// 1, 4, 15, 72, 420
using System; 
 
class GFG
{
     
// Function to find factorial of N
static int factorial(int N)
{
    // base condition
    if( N == 0 || N == 1 )
        return 1; 
    // use recursion 
    return N * factorial( N - 1 );
}
 
// calculate Nth term of series
static int nthTerm(int N)
{
    return (factorial(N) * (N + 2) / 2);
}
 
// Driver Code
public static void Main()
{
    int N = 6;
     
    Console.Write(nthTerm(N));
}
}
 
// This code is contributed by ChitraNayal

PHP

<?php
// PHP program to find
// N-th term of the series:
// 1, 4, 15, 72, 420… 
 
// Function to find factorial
// of N with recursion 
function factorial($N)
{
    // base condition
    if($N == 0 or $N == 1)
        return 1; 
         
    // use recursion 
    return $N * factorial($N - 1);
}
 
// calculate Nth term of series
function nthTerm($N)
{
    return (factorial($N) * 
           ($N + 2) / 2);
}
 
// Driver Code
$N = 6;
 
echo nthTerm($N);
 
// This code is contributed 
// by Shashank
?>

Javascript

<script>
 
// Javascript program to find N-th
// term of the series:
// 1, 4, 15, 72, 420
 
// Function to find factorial of N
function factorial(N)
{
     
    // Base condition
    if (N == 0 || N == 1)
        return 1;
         
    // Use recursion
    return N * factorial(N - 1);
}
 
// Calculate Nth term of series
function nthTerm(N)
{
    return(factorial(N) * (N + 2) / 2);
}
 
// Driver Code
let N = 6;
 
document.write(nthTerm(N));
 
// This code is contributed by avanitrachhadiya2155
 
</script>

Output

Time complexity: O(N)
Auxiliary Space: O(N), for recursion call stack.

Note: Above code wouldn’t work for large values of N. To find the values for large N, use the concept of Factorial for large numbers.

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