Frequency Distribution of Mixed Dice Rolls A follow-up to this challenge
Given a set of mixed dice, output the frequency distribution of rolling all of them and summing the rolled numbers on each die.
For example, consider 1d12 + 1d8 (rolling 1 12-sided die and 1 8-sided die). The maximum and minimum rolls are 20 and 2, respectively, which is similar to rolling 2d10 (2 10-sided dice). However, 1d12 + 1d8 results in a flatter distribution than 2d10: [1, 2, 3, 4, 5, 6, 7, 8, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1] versus [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1].
Rules

The frequencies must be listed in increasing order of the sum to which the frequency corresponds.
Labeling the frequencies with the corresponding sums is allowed, but not required (since the sums can be inferred from the required order).
You do not have to handle inputs where the output exceeds the representable range of integers for your language.
Leading or trailing zeroes are not permitted. Only positive frequencies should appear in the output.
You may take the input in any reasonable format (list of dice ([6, 8, 8]), list of dice pairs ([[1, 6], [2, 8]]), etc.).
The frequencies must be normalized so that the GCD of the frequencies is 1 (e.g. [1, 2, 3, 2, 1] instead of [2, 4, 6, 4, 2]).
All dice will have at least one face (so a d1 is the minimum).
This is code-golf, so the shortest code (in bytes) wins. Standard loopholes are forbidden, as per usual.

Test Cases
These test cases are given as input: output, where the input is given as a list of pairs [a, b] representing a b-sided dice (so [3, 8] refers to 3d8, and [[1, 12], [1, 8]] refers to 1d12 + 1d8).
[[2, 10]]: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
[[1, 1], [1, 9]]: [1, 1, 1, 1, 1, 1, 1, 1, 1]
[[1, 12], [1, 8]]: [1, 2, 3, 4, 5, 6, 7, 8, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1]
[[2, 4], [3, 6]]: [1, 5, 15, 35, 68, 116, 177, 245, 311, 363, 392, 392, 363, 311, 245, 177, 116, 68, 35, 15, 5, 1]
[[1, 3], [2, 13]]: [1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 37, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 1]
[[1, 4], [2, 8], [2, 20]]: [1, 5, 15, 35, 69, 121, 195, 295, 423, 579, 761, 965, 1187, 1423, 1669, 1921, 2176, 2432, 2688, 2944, 3198, 3446, 3682, 3898, 4086, 4238, 4346, 4402, 4402, 4346, 4238, 4086, 3898, 3682, 3446, 3198, 2944, 2688, 2432, 2176, 1921, 1669, 1423, 1187, 965, 761, 579, 423, 295, 195, 121, 69, 35, 15, 5, 1]
[[1, 10], [1, 12], [1, 20], [1, 50]]: [1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 285, 360, 444, 536, 635, 740, 850, 964, 1081, 1200, 1319, 1436, 1550, 1660, 1765, 1864, 1956, 2040, 2115, 2180, 2235, 2280, 2316, 2344, 2365, 2380, 2390, 2396, 2399, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2399, 2396, 2390, 2380, 2365, 2344, 2316, 2280, 2235, 2180, 2115, 2040, 1956, 1864, 1765, 1660, 1550, 1436, 1319, 1200, 1081, 964, 850, 740, 635, 536, 444, 360, 285, 220, 165, 120, 84, 56, 35, 20, 10, 4, 1]
Jelly, &nbsp;14&nbsp; 7 bytes

-3 bytes thanks to Mr. Xcoder (use of an implicit range to avoid leading R; replacement of reduce by the dyadic Cartesian product and flatten, p/F€, with the Cartesian product built-in for that very purpose, Œp.)

ŒpS€ĠL€


A monadic link taking a list of dice faces and returning the normalised distribution of the increasing sums.

Try it online!

How?

Goes through the list of dice "sizes" (implicitly) makes them into their list of faces, then gets the Cartesian product of those lists (all possible rolls of the set of dice), then sums up those rolls, gets the groups of equal indices (by ascending value) and takes the length of each group.

ŒpS€ĠL€ - Link: list of numbers, dice  e.g. [2,5,1,2]
Œp      - Cartisian product (implicit range-ification -&gt; [[1,2],[1,2,3,4,5],[1],[1,2]])
        -                   -&gt; [[1,1,1,1],[1,1,1,2],[1,2,1,1],[1,2,1,2],[1,3,1,1],[1,3,1,2],[1,4,1,1],[1,4,1,2],[1,5,1,1],[1,5,1,2],[2,1,1,1],[2,1,1,2],[2,2,1,1],[2,2,1,2],[2,3,1,1],[2,3,1,2],[2,4,1,1],[2,4,1,2],[2,5,1,1],[2,5,1,2]]
  S€    - sum €ach          -&gt; [4,5,5,6,6,7,7,8,8,9,5,6,6,7,7,8,8,9,9,10]
    Ġ   - group indices     -&gt; [[1],[2,3,11],[4,5,12,13],[6,7,14,15],[8,9,16,17],[10,18,19],[20]]
     L€ - length of €ach    -&gt; [1,3,4,4,4,3,1]


Note: there is only ever one way to roll the minimum (by rolling a one on each and every dice) and we are not double-counting any rolls, so there is no need to perform a GCD normalisation.