Multiplying Arrays

In C and its progeny, array indices start at 0. unsigned long r[5] declares an array of five longs; the array elements are r[0] through r[4]. Your loop, however, varies the array index from 1 though 5. r[5] is accessing whatever happens to lie in memory beyond r[4]

Here is a much better version of your code. Note, among other things, the coding style. Remember that you write programs for other humans to read!

const int kSize = 5;
void setup() {
  unsigned long r[kSize];
  unsigned long product[kSize][kSize];
  unsigned long fact = 1;
  for (int d = 0; d < 5; ++d) {
    fact *= d + 1;
    r[d] = fact;
  }
  for (int row = 0; row < 5; ++row) {
    for (int col = 0; col < 5; ++col) {
      product[row][col] = r[row] * r[col];
    }
  }

  Serial.begin(9600);
  Serial.println("Factorial Table");
  for (int row = 0; row < 5; ++row) {
    for (int col = 0; col < 5; ++col) {
      Serial.print(product[row][col]);
    }
    Serial.println();
  }
}

See the difference? Style points to note:

• no unnecessary comments. In fact, the code is readable enough that no comments are necessary.
• No unnecessary space.
• The array size is used in several places; it's better to define it as a constant. There is also no reason to specify anything other than int; a good optimizer will detect that you are never using values of more than 5, and will optimize the code accordingly.
• You don't really need two separate arrays, since they have the same values.
• You obviously don't need to first store and then print, but I assume you are doing this to learn.
• I didn't initialize the Serial port and didn't print the header until i was ready to print. Group logically-related statements together. (OTOH, you might have been thinking that at some point you might want to insert print statements before there, so putting Serial.begin first thing in your code might have been better.

While there are lots of styles around, https://google.github.io/styleguide/cppguide.html is good enough for Google, so it's good enough for me :)

Here is a better way to initialize the array of factorials:

  r[0] = 1;
  for (int d = 1; d < kSize; ++d) {
    r[d] = r[d - 1] * (d + 1);
  }