This page is under construction.
Soon it will provide more information on the swinging factorial
function. But even now you can find the basics in the The On-Line Encyclopedia of Integer Sequences,
a fantastic database maintained by N. J. A. Sloane.
| n≀ | Type | All | Even | Odd |
| Swinging factorial | seq | A056040 | A000984 | A002457 |
| Binomial transform | seq | A163865 | A026375 | A163869 |
| - " - , triangle | tria | A163840 | A163841 | A163842 |
| - " - , row sums | seq | A163843 | A163844 | A163845 |
| Inverse binomial transform | seq | A163650 | A002426 | A163872 |
| - " - , triangle | tria | A163770 | A163771 | A163772 |
| - " - , row sums | seq | A163773 | A163774 | A163775 |
| Scaled form | tria | A163649 | A098473 | A163945 |
| Odd part of swinging factorial | seq | A163590 | A001790 | A001803 |
| Radical of n≀ is rad(n≀) | seq | A163641 | A080397 | A163640 |
| Primorial(n) / rad(n≀) | seq | A163644 | ||
| Swinging primes | seq | A163074 | ||
| Super swingers | seq | A163085 | ||
| Super duper swingers | seq | A163086 |
Those entries which have a darker background color have been on OEIS before the swinging factorial was introduced. It clearly shows a bias for the even case. Both columns start with family silver type sequences "Formerly M.. N.." (A000984 and A002457).
Divisibility properties of n≀ can be found here.
|
A000120 σ(n) |
A001316 2σ(n) |
A049606 2σ(n)−nn! |
A001147 (2n−1)≀≀ |
Info box: How to write the swinging factorial.
Web designers write ≀ for the symbol ≀. If you use a good browser and have some
good free fonts installed you should have no problem to see n≀ perfectly rendered.
\Te\Xni\cans \mi\ght \use \som\eth\ing \like
"\newcommand{\swing}[1]{\ensuremath{{{#1}\wr}}}".
If you are forced to write with some telegraph code use n$.
Font designers might think of a sacred erected cobra dancing in front of a snake-charmer.
The technical name of the symbol is 'wreath product', the conventional name is
Naja.
More information on math fonts and browsers.
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