About: Mixed factorial

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About: Mixed factorial Sponge Permalink

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Mixed factorial \(n^*\) is a function recursively defined as \[1^* = 1\] \[(n + 1)^* = n^* +^n (n + 1)\] where \(+^n\) is the \(n\)th hyper operator, starting at addition. For example, \(4^* = ((1 + 2) \cdot 3) \uparrow 4\). Informally, the sequence can be visualized as starting with 1 (zero zerated), adding 2, multiplying by 3, exponentiating by 4, tetrating by 5, ... The function was coined by an author under the alias of "SpongeTechX".

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rdfs:label	Mixed factorial
rdfs:comment	Mixed factorial \(n^\) is a function recursively defined as \[1^ = 1\] \[(n + 1)^* = n^* +^n (n + 1)\] where \(+^n\) is the \(n\)th hyper operator, starting at addition. For example, \(4^* = ((1 + 2) \cdot 3) \uparrow 4\). Informally, the sequence can be visualized as starting with 1 (zero zerated), adding 2, multiplying by 3, exponentiating by 4, tetrating by 5, ... The function was coined by an author under the alias of "SpongeTechX".
dcterms:subject	Functions Factorials SpongeTechX
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abstract	Mixed factorial \(n^\) is a function recursively defined as \[1^ = 1\] \[(n + 1)^* = n^* +^n (n + 1)\] where \(+^n\) is the \(n\)th hyper operator, starting at addition. For example, \(4^* = ((1 + 2) \cdot 3) \uparrow 4\). Informally, the sequence can be visualized as starting with 1 (zero zerated), adding 2, multiplying by 3, exponentiating by 4, tetrating by 5, ... The function was coined by an author under the alias of "SpongeTechX".

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