factorial sequence proposal
- From: "wugi" <brol@xxxxxxxxxx>
- Date: Sat, 10 May 2008 16:27:22 +0200
I posted this question to the OEIS
http://www.research.att.com/~njas/sequences/
but didn't get an answer.
I could as well try here, so here my question about a proposed sequence:
<<
I am impressed by the sheer extension of the OEIS database.
I tried to enter the following sequence but I couldn't pass the preview. The
idea of it is simple enough, but as it is about a parametered sequence
(depending on seed n) it's not feasible to fill in with particular values.
I therefore try this way: I'd like to learn if I'm onto a new definition or
in a trodden trail!
The basic idea is, implementing factorials of factorials, or "powered"
factorials.
So I came to use the notation !, !!, !!!, .... !^k, although I found out
that !! is being used for less exciting (in my view) definitions.
A sequence needs a starting number, or seed n : hence,
Seq = Seq(n), with terms a(k)=Seq(n,k) as follows:
a(0) = n
a(1) = n!
a(2) = a(1)! = (n!)! == n!!
......
a(k) = a(k-1)! = n(!!...!!) == n(!^k)
Such sequences, in turn, offer scope for further "supersuperfactorial"
definitions :-o)
I'd appreciate to know if this definition is useful as a new entry, or
indeed exists already somewhere (I myself could not find such definition in
the factorial references I checked).
Some of my amateur's math' themes I put on my webpages
http://home.scarlet.be/~pin12499/qbComplex.html
http://home.scarlet.be/~pin12499/hypereal.htm
http://home.scarlet.be/~pin12499/paratwin.htm
I'd appreciate an expert's comments or advice on those as well "!"
Best regards
guido
.
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