It’s common in programming to use a factorial as a way to teach about recursion. For example, 5! (five factorial) is 5×4×3×2×1, which is 120. Calculating this result can be done with a recursive function, which is practical and satisfying. But mathematicians have a twisted sense of humor, so they invented something called a double factorial. For example: 5!! (five double-factorial) is equal to 5×3×1, which is 15. Because five is an odd number, only odd values are used to calculate the result. Values 4 and 2 are skipped.<\/p>\n Here’s an even parity double factorial calculation:<\/p>\n 8!! = 8×6×4×2 = 384<\/p>\n Only even values are used to obtain the result. Values 7, 5, and 3 are skipped. (Obviously, the final value, one, has no impact on the result.)<\/p>\n When I first encountered the double factorial, I was surprised that the results are less than a single factorial; “double” implies larger, right? Yet, this relationship means that n<\/em>! > n<\/em>!!. I’m uncertain what bearing this effect has, though it’s interesting to note that mathematically n<\/em>! = n<\/em>!! * (n<\/em>-1)!!<\/p>\n For example: 5! = 120. The result of 5!! is 15 and the result of 4!! = 8. Multiply the results together, 15×8, and you get 120, which is 5!.<\/p>\n Enough math!<\/p>\n Your task for this month’s Exercise is to write code that calculates the double factorial of a positive integer. Prompt the use to input a positive integer value. Output the result.<\/p>\n Here’s a sample run from my solution:<\/p>\n To confirm your result, you can visit the Calculator Soup website<\/a>, which features a double factorial calculator.<\/p>\n Please try this challenge on your own before you sneak a look at my solutions<\/a>. One uses a loop and the other uses recursion to calculate the double factorial.<\/p>\n","protected":false},"excerpt":{"rendered":" Just when you think the mathematicians are done, they come up with something else. Continue reading
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\nA double factorial<\/a> works like a factorial, but the results are based on parity of the original value, odd or even. The calculation still involves descending values, just not all of them.<\/p>\nEnter a positive integer: 9
\n9!! = 945<\/code><\/p>\n