Program to find Nth term of series 1, 3, 12, 60, 360…

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

1, 3, 12, 60, 360…

Examples:

Input: 2
Output: 3

Input: 4
Output: 60

Approach: The idea is to first find the factorial of the number (N+1), that is (N+1)!
Now, the N-th term in the above series will be: 

N-th term = (N+1)!/2

Below is the implementation of the above approach:

C++

// CPP program to find N-th term of the series:
// 1, 3, 12, 60, 360…

#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+1
    return fact;
}

// calculate Nth term of series
int nthTerm(int N)
{
    return (factorial(N + 1) / 2);
}

// Driver Function
int main()
{

    // Taking n as 6
    int N = 6;

    // Printing the nth term
    cout << nthTerm(N);

    return 0;
}

C

// C program to find N-th term of the series:
// 1, 3, 12, 60, 360…
#include <stdio.h>

// 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+1
    return fact;
}

// calculate Nth term of series
int nthTerm(int N)
{
    return (factorial(N + 1) / 2);
}

// Driver Function
int main()
{

    // Taking n as 6
    int N = 6;

    // Printing the nth term
    printf("%d",nthTerm(N));

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java program to find N-th
// term of the series:
// 1, 3, 12, 60, 360

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 + 1) / 2);
    }

    // Driver Code
    public static void main(String args[])
    {

        // Taking  n as 6
        int N = 6;

        // Printing the nth term
        System.out.println(nthTerm(N));
    }
}

Python3

# Python 3 program to find
# N-th term of the series:
# 1, 3, 12, 60, 360…

# 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 + 1) // 2)

# Driver code
if __name__ == "__main__" :

    N = 6

    # Function Calling
    print(nthTerm(N))

C#

// C# program to find N-th
// term of the series:
// 1, 3, 12, 60, 360
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 + 1) / 2);
}

// Driver Code
static void Main()
{
    int N = 6 ;

    // Printing the nth term
    Console.WriteLine(nthTerm(N));
}
}

// This code is contributed
// by ANKITRAI1

PHP

<?php
// PHP program to find N-th term
// of the series: 1, 3, 12, 60, 360…

// Function to find factorial of N
function factorial($N)
{
    $fact = 1;

    for ($i = 1; $i <= $N; $i++)
        $fact = $fact * $i;

    // return factorial of N+1
    return $fact;
}

// calculate Nth term of series
function nthTerm($N)
{
    return (factorial($N + 1) / 2);
}

// Driver Code

// Taking n as 6
$N = 6;

// Printing the nth term
echo nthTerm($N);

// This code is contributed
// by chandan_jnu..
?>

Javascript

<script>

// JavaScript program to find N-th term of the series:
// 1, 3, 12, 60, 360…

// 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+1
    return fact;
}

// calculate Nth term of series
function nthTerm(N)
{
    return (Math.floor(factorial(N + 1) / 2));
}

// Driver Function

    // Taking n as 6
    let N = 6;

    // Printing the nth term
    document.write(nthTerm(N));


// This code is contributed by Surbhi Tyagi

</script>

Output:

2520

Time Complexity: O(n), where n represents the given input.
Auxiliary Space: O(1), no extra space is required, so it is a constant.