Catalan-like array with digits

[Marc LeBrun]

Gottfried,

I have not got your question.
Do you ask help in identifying your sequences? If so, did you try to
feed them to Superseeker?

In general, it is hard to guess the nature of a new sequence just from
numerical values. It would make much sense if you provided detailed
description of how to compute the numerical values of your sequence.
The current description ("context") is rather obscure.

Regards,
Max

On 8/20/07, Gottfried Helms <Annette.Warlich at t-online.de> wrote:
> Dear seqfans -
>
> I have a difficult sequence, not in OEIS:
>
> let  n begin at 1, then I have the sequence:
>
> a(n)= 1/2  -1/12  1/48  -1/180  11/8640  -1/6720  -11/241920  29/1451520
>    493/43545600  -2711/239500800  -6203/3592512000  2636317/373621248000
>  -10597579/10461394944000  -439018457/78460462080000 ...
>
> if I rescale
>
>      b(n) = a(n)*n*n! *(n+1)!
>
> I seem to get integers:
>
> b(n)=  1     -1     3     -16     110      -540       -9240      292320
>     14908320      -1639612800      -33013854720        21046667685120
>   -549927873855360          -637881314775344640
>
> another rescaling, perhaps a bit more smooth, is
>
>      c(n) = a(n)*((n+1)!)^2
>
> c(n)= 2     -3    12     -80     660     -3780      -73920     2630880
>     149083200    -18035740800       -396166256640  273606679906560
>     -7698990233975040      -9568219721630169600   ...
>
> I can create this series by matrix-logarithm and exponentiation
> to some finite extent, but to discuss things analytically it would
> be good to have a more direct description.
>
> Someone an idea?
>
>
> Context:
> It occurs in the core of a tetration-formula, where
>
>    f_s:  x:= s^x - 1
>
> and f_s is iterated. The special interest of these coefficients is,
> that they allow to define a powerseries in y,x,log(s) for fractional
> iterates of f_s, where y denotes the fractional value for the iteration.
>
>
> Gottfried
>