Malloc and Jagged arrays in C - c

Question

I'm wrote a program that prints a pyramid of binomial coefficients. The problem is that it prints them correctly when I compile and run the code using Xcode, but it prints wrong numbers when I do so in the terminal. I was hoping someone could tell me why this is happening. I'm running the latest version of Xcode on macOS Mojave.
UPDATE: After relaunching Xcode, I'm not getting the right numbers for the coefficients on Xcode either.
This is the code:
#include <stdio.h>
#include <stdlib.h>
/* Function prototype */
int C(int a, int b);
int main(){
int count =0;
int n = 0; /* The number of rows in the array (minus 1) */
/* Prompt user to input and validate */
printf("Please enter a positive integer:\n"
"n = ");
do
scanf("%d", &n);
while ( n <= 0 );
/* Allocate enough memory for the matrix */
int **matrix = (int**) malloc( (n+1) * sizeof(int*) );
/* Allocate enough memory for each array */
for (int i = 0; i < n+1; i++) {
matrix[i] = (int*) malloc( (i+1) * sizeof(int) );
}
/* Populate each array */
for (int i = 0; i < n+1; ++i) {
for (int j = 0; j < i+1; ++j) {
matrix[i][j] = count;
count++;
}
}
/* Print pyramid */
for (int i = 0; i < n+1; ++i) {
for (int j = 0; j < i+1; ++j) {
if ( (i==0) && (j==0) ) {
for (int k = 0; k < n+1-i; ++k) {
printf("\t");
}
printf("%d\n", matrix[i][j]);
}
else
if (j == 0) {
for (int k = 0; k < n+1-i; ++k) {
printf("\t");
} printf("%d\t", matrix[i][j]);
} else
if ( (0 < j) && (j < i) ) {
printf("\t%d\t", matrix[i][j]);
}
else
if (j == i) {
printf("\t%d\n", matrix[i][j]);
}
}
}
/* Free allocated memory */
free(matrix);
return 0;
}
/************************ Function Definition **********************/
/*
* Function: C
* -----------
* Computes the binomial coefficient via the factorial formula, using
* for-loops for the factorials.
*
* f_a = the factorial of the first number
* f_b = the factorial of the other number
* f_a_b = the factorial of the difference (a-b)
*
* returns: the binomial C = (a,b)
*/
int C(int a, int b) {
unsigned int f_a = 1;
unsigned int f_b = 1;
unsigned int f_a_b = 1;
for ( int i = 1; i < a; ++i ) {
f_a *= i;
}
for ( int i = 1; i < b; ++i ) {
f_b *= i;
}
for ( int i = 1; i < (a-b); ++i ) {
f_a_b *= i;
}
unsigned int C = f_a / ( f_b * f_a_b );
return C;
}

Answer 1

The way you compute the factorials is wrong:
for ( int i = 1; i < a; ++i )
should be
for ( int i = 1; i <= a; ++i )
since you have to include the last element. Thats the way the factorial is defined.
Also this function is more suitable to calculate binomial coefficients since the factorial overflows at 13 (with 32 bit int).
int C(int a, int b)
{
int bc = 1;
if (b > a-b)
{
b = a-b;
}
for (int i = 0; i < b; i++)
{
bc *= (a - i);
bc /= (i + 1);
}
return bc;
}