[seqfan] Re: My tool for exploring sequences

[Thomas Baruchel]

On Sat, 19 Dec 2015, Alexander Povolotsky wrote:
> Hi Dear Thomas,
>
> Could You share results, which you have obtained using your tool?

Hi, I am going to leave my home for the holidays, but very quickly, I
take a sequence I contributed some months ago, which is: A108626
(I didn't try many sequences for the current reply; I really picked this
one at first by hoping it could give something interesting).

I type:

java -jar target/oeis-deconvolution2-1.0.0-standalone.jar -d \
../oeis-deconvolution/stripped.gz "1, 2, 5, 14, 41, 124, 383, 1200, \
3799, 12122, 38919, 125578, 406865, 1322772, 4313155, 14099524"

Among the printed results, one seems interesting because it has a lower
norm than other results:

> Deconvolution with A036217:
>  is (1 -13 65 -151 146 -14 -28 0 -8 -16 -18 -26 -40 -60 -86 -98)
>  --> norm is 73012

Superseeker tells me that the sequence above has LDOGF:

   - (-13/3+52/3*x-8*x^2-2/3*x^3-3*x^4)/(x^5-1/3*x^4+2*x^3-14/3*x^2+7/3*x-1/3)

A036217 is:         Expansion of 1/(1-3*x)^5

Now, I open Pari-GP and type:

   (exp(-log(x^3+x^2+3*x-1)/2+5*log(3*x-1)-log(x-1)/2))/ (1-3*x)^5

and obviously this is a (new?) generating function for A108626

Best regards,

-- 
Thomas Baruchel