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A191379
Expansion of product(n>=0, 1+2*x^(3^n)+x^(2*3^n)+2*x^(3*3^n)+x^(4*3^n) ).
This is an analog of the classical Stern sequence (A002487) with generating function product(n>=0, 1+x^(2^n)+x^(2*2^n) ).
The author of the linked paper proves that the sequence {a(n)/a(n+1)} enumerates the set of positive rational numbers with either an even numerator or an even denominator.