[seqfan] On Fabius function

Juan Arias de Reyna arias at us.es
Sat Jun 3 19:57:31 CEST 2017


Dear sqfans,

I want to include a sequence of rational numbers d(n)=a(n)/b(n) in OEIS.
This sequence is related to the values of the Fabius function  F(x) by

d(n)=n! 2^binomial(n,2) F(2^(-n)). 

Not very surprisingly I find that the numerators a(n) appear to coincide 
with A272755: numerators of the Fabius function F(1/2^n).  But I have no 
proof that  n! 2^binomial(n,2) divides the denominator of  F(1/2^n).
(I have checked the equality of numerators for 0 <= n <=  200)

Should I include then a sequence that will appear as a duplicate of A272755
with a different definition?  Adding then a conjecture. 

Should I include only the denominators of the d(n)?

What is the correct procedure here?

Thanks for your attention,
Juan Arias de Reyna





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