Metadata
bibkey: hanna2024a374570
authors: Paul D. Hanna
year: 2024
title: OEIS A374570, g.f. satisfying A(x)^2 = A(A(x)*C(x)) with C the Catalan function
doi: null
url: https://oeis.org/A374570
claim: "Expansion of g.f. A(x) satisfying A(x)^2 = A( A(x)*C(x) ), where C(x) = x + C(x)^2 is the Catalan function (A000108). Conjecture: for n > 1, a(n) is odd iff n = 2^k + 1 for k >= 0."
strata_touched:
- D5/S1/Recurrence/Invariants/CatalanCompositionSquareParity
license: citation-only
triage: anchor
OEIS A374570
Paul D. Hanna’s entry of July 11, 2024 gives the generating equation and the parity conjecture quoted above. The normalization is A(0) = 0 and a(1) = 1. The shifted Catalan series C has constant coefficient zero. The Lean module constructs the normalized integer solution, proves its uniqueness, and proves the parity characterization for every n > 1.
Verified locator
- URL: https://oeis.org/A374570