Answer 1

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène CharlesCatalan (1814–1894).
Code:
static void Main(string[] args)
{
int i, n, fact, fact1, fact2, CatalanN; Console.WriteLine("Enter a Number (n>=0)");
n = Convert.ToInt32(Console.ReadLine()); fact = n;
for (i = n - 1; i > 0; i--)
{
fact = fact * i;
}
Console.WriteLine("" + fact);
Console.ReadLine();
fact1 = 2*n;
for (i = 2*n - 1; i > 0; i--)
{
int old = fact1;
fact1 = fact1 * i;
Console.WriteLine("" + old + " " + fact1);
}
Console.ReadLine();
fact2 = n+1;
for (i = (n+1)-1; i > 0; i--)
{
fact2 = fact2 * i;
}
Console.WriteLine("" + fact2);
Console.ReadLine();
CatalanN = fact1 / (fact2 * fact); Console.WriteLine("Catalan Number of the given number is : " + CatalanN);
Console.ReadLine();
}