nth_catalan

/**
 *    author:  math2do
 *    created: 02.05.2020 14:06:08 IST
**/

#include <bits/stdc++.h>

using namespace std;

using ull = unsigned long long int;
const int N = 100;
vector <ull> catalan(N + 1);

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  auto calc = [&] () {
    catalan[0] = catalan[1] = 1;
    for (int i = 2; i <= N; i++) {
      catalan[i] = 0;
      for (int j = 0; j < i; j++) {
        catalan[i] += catalan[j] * catalan[i - j - 1];
      }
    }
  };
  calc();

  // now catalan[n] gives nth catalan number
  return 0;
}