Narayana number in C++

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The Narayana numbers can be expressed in terms of binomial expression $1/n\binom{n}{k} \binom{n}{k-1}$  Learn more about the Narayana number here.

You are given the numbers n and k. Find the Narayana number. It's a straightforward problem having the combinations formula. Let's see the code.


  • Initialise the numbers n and k.
  • Find the Narayana number using the given formula.
  • Print the resultant number.


Following is the implementation of the above algorithm in C++

#include <bits/stdc++.h>
using namespace std;
int factorial(int n) {
   int product = 1;
   for (int i = 2; i <= n; i++) {
      product *= i;
   return product;
int nCr(int n, int r) {
   return factorial(n) / (factorial(n - r) * factorial(r));
int main() {
   int n = 8, k = 5;
   cout << nCr(n, k) * nCr(n, k - 1) / n << endl;
   return 0;


If you run the above code, then you will get the following result.

Updated on 23-Oct-2021 07:11:21