Numerator of $\binom{6n-2}{2n} / \left(2 \binom{4n-1}{2n}\right)$

formal-conjectures · oeis · ams-11

Conjecture: $\binom{6n-2}{2n} / \left(2 \binom{4n-1}{2n}\right) = A005156(n+1)/A005156(n)$

It is conjectured that
$\binom{6n-2}{2n} / \left(2 \binom{4n-1}{2n}\right) = A005156(n+1)/A005156(n)$,
where the OEIS comment reads A005156 as 1-based; with the 0-indexed b this is
frac (n + 1) = b (n + 1) / b n.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A109074
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/109074.lean
Local target: Corpus.OEIS109074.conjecture
Source SHA-256: 6c3144b835a4c5c5a354dffebb5f3e2847dc95f3339db85cd25c8fcc8d20622c
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record