A120011 and A127275
Max Alekseyev
maxale at gmail.com
Tue Jun 17 18:36:11 CEST 2008
Actually, the generating function listed in A120011 is not reduced
(the numerator and denomerator share the common factor 1-4x):
A(x) = x*(3 - 12*x - 2*(1-4*x)*C(x) ) / (1-4*x)^2 = (3*x - 2*x*C(x)) / (1-4*x)
Plugging in C(x) = (1-sqrt(1-4*x))/(2*x) results in:
A(x) = (3*x - 1 + sqrt(1-4*x)) / (1-4*x) = -1 + (sqrt(1-4*x) - x)/(1-4*x)
which proves the specified relationship between A120011 and A127275.
I think A120011 can be simply removed in favor of the following
comment to A127275:
%C A127275 The 2-nd self-compose of g.f. G(x) of A120009 is G(G(x)) =
(sqrt(1-4x)-x)/(1-4x) - 1.
Regards,
Max
On Sat, Jun 14, 2008 at 12:18 PM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
>
> Given that A127275 and A120011 are almost the same, and that the
> generating functions are described in some detail, it seems to be manageable
> to simplify A120011 based on this, and to show that they only differ
> by the additional leading number in A127275.
>
> Richard
>
Richard:
Thanks very much for editing all those sequences!
I appreciate your help (and Maximilian's)
New version of the OEIS with all these
entries in a few minutes
(except I have not finished reading emails from the
past week, so there may be more in the pipeline)
By the way, this person submitted a lot more entries,
of the same type, and still not using the web page.
I rejected them, and told him I could not accept
(Since they were all very uninteresting sequences,
- just as the ones you edited turned out in the end
not to be very interesting -
I figured there would be no loss if he did not do so)
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