My favorite integer sequence

[Gottfried]

It took just 2.5 minutes to calculate the polynomials, about twice as fast as SAGE/python, if I recall correctly. Not sure why the difference, but I'm not complaining:

Here is the second draft of the pari/gp code to calculate the sequence:


I tried my hand at Newton's method, using Stirling numbers of the first kind, and the increase in speed is incredible. It took 2.5 minutes to calculate the first 100 polynomials in the previous version. Now it takes about 10 seconds!!

(...)

Thanks for that scripts. that shall help me much to get experienced with the computation-idea. Everything went well, except that with my Pari/GP-version I had to introduce "listcreate" and could not apply multiple case-selection in the if()-procedure.
Here are some of my timings:

InitPolys(10) \\ 15 ms
InitPolys(20) \\ 31 ms
InitPolys(30) \\ 172 ms
InitPolys(40) \\ 577 ms
InitPolys(50) \\ 1,716 ms
InitPolys(60) \\ 4,649 ms
InitPolys(70) \\ 8,954 ms
InitPolys(100) \\ 52,041 ms

A(2^100) \\ 7,769 ms


Gottfried