Hyperfactorial

The function defined by

$$H(n)\equiv K(n+1)\equiv 1^1 2^2 3^3\cdots n^n,$$

where $K$ is the K-Function and the first few values for $n = 1$, 2, ... are 1, 4, 108, 27648, 86400000, 4031078400000, 3319766398771200000, ... (Sloane's A002109), and these numbers are called hyperfactorials by Sloane and Plouffe (1995).

See also G-Function, Glaisher-Kinkelin Constant, K-Function

References

Sloane, N. J. A. Sequence A002109/M3706 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.