Talk about A020995

[y.kohmoto]

    ID Number: A020955
    URL:       http://www.research.att.com/projects/OEIS?Anum=A020955
    Sequence:  0,1,2,81,4194304,1490116119384765625,
               226267027688376192080197927193400943822503936,

2580862109893492760479178174131723836316911402760995479112805984259278534373
    Name:      n^(2^n-n-1).
    Comments:  Number of finite models of natural number on the free class
with n
                    members.
    Links:     Yasutoshi Kohmoto, The other Side of Mathematics
    Example:   For n=2, a(2)=2, universe class={0,1}.
               1 : { }ma 0, {0}ma 1, {0,1}ma 1, {1}ma 0,
               2 : { }ma 0, {0}ma 1, {0,1}ma 1, {1}ma 1.

    To Neil :
    I found this sequence on OEIS.

    I have thought that you rejected it when I posted it .
    Does it mean  that you understand my set theory "Free Class"?
    If "Yes", then you are one of four persons who understand Free Class.
    It is nice!!

    Four people :
    You,

    Randall Holmes,
    http://math.boisestate.edu/~holmes/holmes/nf.html
    He said "Your dissolution about Russel's paradox seems to be correct."

    Karlis Podnieks,
    http://www.ltn.lv/~podnieks/
    He said " It is a promising idea."

    Yasumi Kobayasi,
    http://web.kyoto-inet.or.jp/people/kbys_ysm/
    Yasumi is my friend who is a writer scientist
    He said " It is great."

    I want to know your opinion about Free Class.

    Or,

    Does any sequence which you don't understand exist on OEIS?

    The sequence is essentially number of mapping from 2^X to X.
    Where X is a finite set whose member is n.

    The sequence becomes :

    s(n) :
    0, 1, 16, 6561, 4294967296, 23283064365386962890625,
    63340286662973277706162286946811886609896461828096,

1487815647197611695910312681741273570332356717154798949898498305086387315423
300999654757561928633305897036801

    Formula : n^(2^n)
    It doesn't exist on OEIS.

    -(n+1) in the name of A020995 means that (n+1) part classes of 2^X are
decided with the condition of natural number's model.
    Some explanations of Free Class is available on my home page.

    To browse my home page has a little problem.
    You must have Japanese character set.
    I used many two bytes code's "space" in the sentences, they are
invisible on Japanese editor.
    And they were transformed to unreadable character in one byte code.
    If you use Japanese character set, then they will disappear.


    Correction :
    The link on %Y line of A020995 is as follows.
         http://boat.zero.ad.jp/~zbi74583/another02.htm

    Yasutoshi