Subfactorial/Examples/5
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Example of Subfactorial
- $!5 = 44$
Proof
| \(\ds !5\) | \(=\) | \(\ds 5! \paren {1 - \dfrac 1 {1!} + \dfrac 1 {2!} - \dfrac 1 {3!} + \dfrac 1 {4!} - \dfrac 1 {5!} }\) | Definition of Subfactorial | |||||||||||
| \(\ds \) | \(=\) | \(\ds 120 \paren {1 - \dfrac 1 1 + \dfrac 1 2 - \dfrac 1 6 + \dfrac 1 {24} - \dfrac 1 {120} }\) | Examples of Factorial | |||||||||||
| \(\ds \) | \(=\) | \(\ds 120 \paren {\dfrac {60 - 20 + 5 - 1} {120} }\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 44\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $44$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $44$