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With the 'cancelling out' you've performed on the constants in your ex_*() subs, I couldn't see the pattern by which they were derived.
Undoing that, I now see that they come (directly or not) from Pascal's Triangle.
I guess at some point I should review some teaching materials to understand why those constants are used here, but for now it is enough to know that I can now write a generic ex_*() function (generator). Thanks.
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