Hyperfactorial

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In mathematics, the hyperfactorial is a function on natural numbers that is related to the factorial. Generally written as H(n), it is defined as

For n = 1, 2, 3, 4,... the values of H(n) are 1, 4, 108, 27648,... (sequence A002109 in OEIS).

The hyperfactorial function is similar to the factorial, but produces larger numbers. The rate of growth of this function, however, is not much larger than a regular factorial. However, H(14) = 1.847398448... x 10⁹⁹ is already almost equal to a googol, and H(15) = 8.08964493... x 10¹¹³ is almost of the same magnitiude as the Shannon number, the theoretical number of possible chess games.

The hyperfactorial function can be generalized to complex numbers in a similar way as the factorial function; the resulting function is called the K-function.