19 lines
1.1 KiB
Plaintext
19 lines
1.1 KiB
Plaintext
The factorial of a number, written as <math>n!</math>, is defined as <math>n! = n(n-1)(n-2)...(2)(1)</math>.
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[http://mathworld.wolfram.com/Multifactorial.html Multifactorials] generalize factorials as follows:
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: <math>n! = n(n-1)(n-2)...(2)(1)</math>
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: <math>n!! = n(n-2)(n-4)...</math>
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: <math>n!! ! = n(n-3)(n-6)...</math>
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: <math>n!! !! = n(n-4)(n-8)...</math>
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: <math>n!! !! ! = n(n-5)(n-10)...</math>
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In all cases, the terms in the products are positive integers.
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If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
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# Write a function that given n and the degree, calculates the multifactorial.
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# Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
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'''Note:''' The [[wp:Factorial#Multifactorials|wikipedia entry on multifactorials]] gives a different formula. This task uses the [http://mathworld.wolfram.com/Multifactorial.html Wolfram mathworld definition].
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