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Metadata 
bibkey: hanna2023a363308
authors: Paul D. Hanna
year: 2023
title: OEIS A363308, expansion of C(x*C(x)^3) with C the Catalan g.f.
doi: null
url: https://oeis.org/A363308
claim: "Expansion of g.f. C(x*C(x)^3), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108). Conjecture: a(n) is odd iff n is a power of 2 or n = 0."
strata_touched:
  - D5/S1/Recurrence/Invariants/CatalanCubicCompositionParity
license: citation-only
triage: anchor

OEIS A363308

Paul D. Hanna’s entry, dated May 28, 2023, defines the sequence by the Catalan composition C(x*C(x)^3) and states the quoted parity conjecture. The Lean module constructs this composition from the Catalan numbers, proves its generating equation, and proves the conjecture for every natural index, including zero.

Verified locator

  • URL: https://oeis.org/A363308