Definition:Subfactorial/Sequence
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Examples of Factorials
The sequence of subfactorials begins:
$\begin{array}{r|r} n & !n \\ \hline 0 & 1 \\ 1 & 0 \\ 2 & 1 \\ 3 & 2 \\ 4 & 9 \\ 5 & 44 \\ 6 & 265 \\ 7 & 1 \, 854 \\ 8 & 14 \, 833 \\ \end{array}$
This sequence is A000166 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Examples
Subfactorial of $4$
- $!4 = 9$
Subfactorial of $5$
- $!5 = 44$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $44$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $44$