Definition:Subfactorial/Sequence

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): $44$