Consider the following sequence defined by:

\[ U_0=1 ; U_n= \Big\{\begin{array}{c c c} U_{n-1}^2 & if & \texttt{n is an even number } \\ U_{n-1}+n! & if & \texttt{n is an odd number} \end{array}\]

• Write a function that takes an integer n as parameter, and returns the corresponding value of $$U_n$$.
• Write a function that takes as parameter an integer X, and prints the greatest value of n such that $$U_n \leq X$$

#include <stdio.h>
#include <math.h>

int fact(int n)
{
    if(n==0) return 1;
    return n * fact(n-1);
}

int sequence(int n)
{
    if(n==0) return 1;
    if(n%2) return sequence(n-1)+fact(n);
    return pow(sequence(n-1),2);
}

int closest(int x)
{
    int i=1;
    while(sequence(i)<x)
        i++;
    return i-1;
}

int main()
{
    printf("sequence(4)=%d\n",sequence(4));
    printf("sequence(5)=%d\n",sequence(5));
    printf("closest(230)=%d\n",closest(230));
    return 0;
}