bibkey: hanna2026a393170 authors: Paul D. Hanna year: 2026 title: OEIS A393170, self-referential inverse series doi: null url: https://oeis.org/A393170 claim: “For A(x)=sum a(n)x^n defined by [x^n]1/(A(x)-n*x)=0 for n>=1, a(n) is odd iff n is a power of two for n>0.” strata_touched:

• D5/S3/Arith/SelfReferentialInverseSeriesParity license: citation-only triage: anchor

OEIS A393170

Paul D. Hanna’s entry fixes a(0) = 1 and defines the remaining coefficients of the integer formal power series by requiring the degree-n coefficient of 1/(A(x)-n*x) to vanish for every positive n. It states that the positive-index coefficients are odd exactly at powers of two. The module’s h0 : constantCoeff A = 1 records this stated normalization; it is not an additional restriction on the sequence described by the entry.

Verified locator

• URL: https://oeis.org/A393170