[seqfan] Name of sequence A105609

[JUAN ARIAS DE REYNA MARTINEZ]

The sequence A105609 is defined as "Sylvester numbers for 1/(1+x^2)" There are two links in  this entry, one to a paper of Peter Luschny and Stefan Wehmeier in which the word Sylvester do not appear. Then to a page of Eric Weisstein's World of Mathematics "Sylvester cyclotomic Number" that again do not give any reason for Sylvester name, and less of the function 1/(1+x^2), also I do not see the relation of this page with the sequence A105609. 

Does anyone know the reason for the name?
What does Sylvester have to do with it and what are the Sylvester numbers for f(x)?


Thanks in advance 

Juan Arias de Reyna