# [seqfan] Re: "A dream" of a series :-)

Maximilian Hasler maximilian.hasler at gmail.com
Sun Feb 15 14:07:45 CET 2009

```Very nice article.
Just, for the next update, you may want to fix the numerical data at
the very beginning of the article:

exp(x+O(x^9))
%1 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 +
1/5040*x^7 + 1/40320*x^8 + O(x^9)

%/(1+x)
%2 = 1 + 1/2*x^2 - 1/3*x^3 + 3/8*x^4 - 11/30*x^5 + 53/144*x^6 -
103/280*x^7 + 2119/5760*x^8 + O(x^9)

%/(1+x^2/2)
%3 = 1 - 1/3*x^3 + 3/8*x^4 - 1/5*x^5 + 13/72*x^6 - 15/56*x^7 +
533/1920*x^8 + O(x^9)

and not -3/8 x^3 as written in the article.
Regards,
Maximilian

On Sun, Feb 15, 2009 at 3:16 AM, Gottfried Helms
<Annette.Warlich at t-online.de> wrote:
> Dear seqfans -
>
>  there was no time in summer, when I discussed this
>  "dream of a series". In the meantime I could put things
>  together into a short readable article.
>  Hope you enjoy!
>
>    http://go.helms-net.de/math/musings/dreamofasequence.pdf
>
>  The main sequence exists in OEIS (A067911, (*1)) although
>
>  - not with the relation to the generating process as described
>     in the article (I'll supply that information soon)
>
>  - modified in the sense, that in my article the sequence
>     is defined by denominators of rational numbers and some
>     missing primefactors may be seen as cancelled by the numerators
>     of the coefficients by the rational-arithmetic-system in Pari/GP.
>
>  If I want to add the numerator-sequence to OEIS we must decide,
>  whether I expand my numerators such that the denominators match
>  the values in A067911 or whether I should send numerators and
>  denominators in their reduced versions.
>  Neill - what's your opinion?
>
> Gottfried Helms
>
>
> (*1)  http://www.research.att.com/~njas/sequences/A067911
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```