The double factorial is an extension onto the normal factorial function. It is denoted with two exclamation points: . Do not confuse the double factorial for a factorial computed twice. The double in double factorial represents the increment between the values of the terms when the factorial is expanded into a product. In the case of a regular factorial, each factor is decremented by one, from the number 'a' to 1. In the case of a double factorial, each factor is decremented by two. The double factorial terminates with the sequence of evens, for example: or the sequence of odds: eg where
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| - The double factorial is an extension onto the normal factorial function. It is denoted with two exclamation points: . Do not confuse the double factorial for a factorial computed twice. The double in double factorial represents the increment between the values of the terms when the factorial is expanded into a product. In the case of a regular factorial, each factor is decremented by one, from the number 'a' to 1. In the case of a double factorial, each factor is decremented by two. The double factorial terminates with the sequence of evens, for example: or the sequence of odds: eg where
- The double factorial is a version on the factorial, defined as \(n!! = n \cdot (n - 2) \cdot (n - 4) \cdot \ldots\). In other words, it is made by multiplying all the positive odd numbers up to n if n is odd, or multiplying all the positive even numbers up to n if n is even. The first few values of \(n!!\) for \(n\) = 0, 1, 2, 3, ... are 1, 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, ... (OEIS A006882) The sum of the reciprocals of these numbers is 2.059407405342577... When \(n\) is even, \(n!! = (\frac{n}{2})! 2^{(\frac{n}{2})}\).
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| - The double factorial is an extension onto the normal factorial function. It is denoted with two exclamation points: . Do not confuse the double factorial for a factorial computed twice. The double in double factorial represents the increment between the values of the terms when the factorial is expanded into a product. In the case of a regular factorial, each factor is decremented by one, from the number 'a' to 1. In the case of a double factorial, each factor is decremented by two. The double factorial terminates with the sequence of evens, for example: or the sequence of odds: eg where The following properties hold: for any integer There also exists the triple factorial, which is not as commonly known or used as the double, and with it a set of of analogous properties.
- The double factorial is a version on the factorial, defined as \(n!! = n \cdot (n - 2) \cdot (n - 4) \cdot \ldots\). In other words, it is made by multiplying all the positive odd numbers up to n if n is odd, or multiplying all the positive even numbers up to n if n is even. The first few values of \(n!!\) for \(n\) = 0, 1, 2, 3, ... are 1, 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, ... (OEIS A006882) The sum of the reciprocals of these numbers is 2.059407405342577... When \(n\) is even, \(n!! = (\frac{n}{2})! 2^{(\frac{n}{2})}\). It should be noted that \(n!!\) is not equivalent to \((n!)!\) (nested factorial). Double factorial actually grows slower than factorial.
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