Swinging Factorial

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.

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 medieval 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.

Once again the Windows Internet Explorer fails. In this case switch to Firefox and get this information on fonts.