﻿ Swinging Factorial

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 &#x2240; 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.