Standalone experimentation with rolling n dice with s sides.

Dice.java

import java.util.Map;
import java.util.SortedMap;
import java.util.TreeMap;

public class Dice {
	public static void main(String[] args) {
		SortedMap<Long, Long> zeroSixSidedDice = sumOccurrencesOfDiceRoll(6, 0);
		SortedMap<Long, Long> singleSixSidedDie = sumOccurrencesOfDiceRoll(6, 1);
		SortedMap<Long, Long> twoSixSidedDice = sumOccurrencesOfDiceRoll(6, 2);
		SortedMap<Long, Long> threeSixSidedDice = sumOccurrencesOfDiceRoll(6, 3);

		assert zeroSixSidedDice.values().stream().mapToLong(Long::longValue).sum() == 1;
		assert singleSixSidedDie.values().stream().mapToLong(Long::longValue).sum() == 6;
		assert twoSixSidedDice.values().stream().mapToLong(Long::longValue).sum() == 6 * 6;
		assert threeSixSidedDice.values().stream().mapToLong(Long::longValue).sum() == 6 * 6 * 6;
	}

	private static SortedMap<Long, Long> sumOccurrencesOfDiceRoll(long sides, long dice) {
		if (dice < 0) throw new IllegalArgumentException("Must have 0 or more dice");
		if (sides < 1) throw new IllegalArgumentException("Dice must have at least one side");

		SortedMap<Long, Long> sums = new TreeMap<>();

		if (dice == 0) {
			sums.put(0L, 1L);
			return sums;
		}

		for (long i = 1; i <= sides; i++) {
			sums.put(i, 1L);
		}

		for (long i = 2; i <= dice; i++) {
			SortedMap<Long, Long> next = new TreeMap<>();

			for (Map.Entry<Long, Long> entry : sums.entrySet()) {
				long sum = entry.getKey();
				long occurrences = entry.getValue();

				for (long possibleRoll = 1; possibleRoll <= sides; possibleRoll++) {
					next.compute(sum + possibleRoll, (key, old) -> {
						if (old == null) return occurrences;

						return old + occurrences;
					});
				}
			}

			sums = next;
		}

		return sums;
	}
}