Ultrafactorial

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$U(n)\equiv {n!}^{n!},n\geq 0.\,$

The ultrafactorial numbers give the sequence (Cf. A046882)

{1, 1, 4, 46656, 1333735776850284124449081472843776, ...}

Higher order ultrafactorials

$U_{0}(n)\equiv 1,\quad n\geq 0.\,$ (empty product, defined as the multiplicative identity, i.e. 1)

$U_{1}(n)\equiv {n!},\quad n\geq 0.\,$ (factorial)

$U_{2}(n)\equiv {n!}^{n!},\quad n\geq 0.\,$ (ultrafactorial)

$U_{3}(n)\equiv {n!}^{{n!}^{n!}},\quad n\geq 0.\,$

$U_{4}(n)\equiv {n!}^{{n!}^{{n!}^{n!}}},\quad n\geq 0.\,$

...

See also

• Factorial
• Ultraprimorial