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 2 ^{σ(n)} |
A049606 2 ^{σ(n)−n}n! |
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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